title: The Schr\"odinger Functional for Improved Gluon and Quark Actions

abstract:
  The Schr\"odinger Functional (quantum/lattice field theory with Dirichlet
boundary conditions) is a powerful tool in the non-perturbative improvement and
for the study of other aspects of lattice QCD. Here we adapt it to improved
gluon and quark actions, on isotropic as well as anisotropic lattices.
Specifically, we describe the structure of the boundary layers, obtain the
exact form of the classically improved gauge action, and outline the
modifications necessary on the quantum level. The projector structure of
Wilson-type quark actions determines which field components can be specified at
the boundaries. We derive the form of O(a) improved quark actions and describe
how the coefficients can be tuned non-perturbatively. There is one coefficient
to be tuned for an isotropic lattice, three in the anisotropic case.
  Our ultimate aim is the construction of actions that allow accurate
simulations of all aspects of QCD on coarse lattices.


title: O(a) improved lattice QCD

abstract:
  We review the O(a) improvement of lattice QCD with special emphasis on the
motivation for performing the improvement programme non-perturbatively and the
general concepts of on-shell improvement. The present status of the
calculations of various improvement coefficients (perturbative and
non-perturbative) is reviewed, as well as the computation of the isospin
current normalization constants $Z_A$ and $Z_V$. We comment on recent results
for hadronic observables obtained in the improved theory.


title:
The phase diagram of the $U(2) \times U(2)$ Sigma Model and its
  Implications for Chiral Hierarchies

abstract:
  Motivated by the issue of whether it is possible to construct
phenomenologically viable models where the electroweak symmetry breaking is
triggered by new physics at a scale $\Lambda \gg 4\pi v$, where $v$ is the
order parameter of the transition ($v\sim 250$ GeV) and $\Lambda$ is the scale
of new physics, we have studied the phase diagram of the $U(2) \times U(2)$
model. This is the relevant low energy effective theory for a class of models
which will be discussed below. We find that the phase transition in these
models is first order in most of parameter space. The order parameter can not
be made much smaller than the cut-off and, consequently a large hierarchy does
not appear sustainable. In the relatively small region in the space of
parameters where the phase transition is very weakly first order or second
order the model effectively reduces to the O(8) theory for which the triviality
considerations should apply.


title: QCDSP: The first 64 nodes

abstract:
  We present a summary of the progress on QCDSP in the last year. QCDSP,
Quantum Chromodynamics on Digital Signal Processors, is an inexpensive computer
being built at Columbia that can achieve 0.8 teraflops for three million
dollars.


title: Dependence of QCD hadron masses on the number of dynamical quarks

abstract:
  We have studied the hadron spectrum while varying the number of light
dynamical quarks when the physical lattice spacing and volume are held fixed
relative to the rho mass. For two and zero flavors of staggered fermions, we
find the nucleon to rho mass ratios (extrapolated to zero valence quark mass)
are very similar. However, for four flavors the ratio is 7% (2 standard
deviations) above the two flavor result.


title: Lattice QCD with 0, 2 and 4 quark flavors

abstract:
  We have done simulations of lattice QCD with different numbers of light
dynamical quarks. Since we cannot reach the continuum limit with our current
computers, we have done comparisons with 0 (quenched), 2 and 4 light quark
flavors with the physical volume and lattice spacing constant, when these are
determined from the mass of the rho. We find a 7% (2 standard deviation)
difference in the nucleon to rho mass ratio for 2 and 4 quarks. More
importantly, the effects of chiral symmetry breaking are dramatically decreased
for the case of 4 light quarks.


title: Evidence for pronounced quark loop effects in QCD

abstract:
  We have measured the hadron spectrum in lattice QCD, using staggered
fermions, for 0 (the quenched approximation), 2 and 4 light degenerate
dynamical quarks. In addition to earlier results involving extrapolations in
valence quark masses for fixed dynamical mass, we also report results where we
extrapolate in the dynamical mass for 4 flavors. We see a marked difference in
the hadron spectrum for 2 and 4 flavors; the hadron spectrum is nearly parity
doubled for 4 flavors, indicating smaller effects of chiral symmetry breaking.
This pronounced effect in the hadron spectrum cannot be removed by a simple
change in scale as the number of light quark flavors is changed. Further
simulations at larger volume are needed to rule out finite volume effects.


title: Field strength correlators in full QCD

abstract:
  We study, by numerical simulations on a lattice, the behaviour of the
gauge-invariant two-point correlation functions of the gauge field strengths in
the QCD vacuum with dynamical fermions.


title: Flux-tube structure and beta-functions in SU(2)

abstract:
  The spatial distribution of the action and energy in the colour fields of
flux-tubes is studied in lattice SU(2) field theory for static quarks at
separations up to 1 fm at beta=2.4, 2.5. The ground and excited states of the
colour fields are considered. Sum rules are used to get estimates of
generalised beta-functions.


title: Leptonic Decays of Heavy Quarks on the Lattice

abstract:
  The status of lattice calculations of heavy-light decay constants and of the
$B$ parameter $B_B$ is reviewed. After describing the lattice approach to heavy
quark systems, the main results are discussed, with special emphasis on the
systematic errors in present lattice calculations. A detailed analysis of the
continuum limit for decay constants is performed. The implications of lattice
results on studies of CP violation in the Standard Model are discussed.


title:
Lattice QCD Calculation of the Kaon B-parameter with the Wilson Quark
  Action

abstract:
  The kaon B parameter is calculated in quenched lattice QCD with the Wilson
quark action. The mixing problem of the \Delta s=2 four-quark operators is
solved non-perturbatively with full use of chiral Ward identities, and this
method enables us to construct the weak four-quark operators exhibiting good
chiral behavior. We find B_K(NDR, 2GeV)=0.562(64) in the continuum limit, which
agrees with the value obtained with the Kogut-Susskind quark action.


title:
Perturbative Renormalization Factors of Bilinear Operators for Massive
  Wilson Quarks on the Lattice

abstract:
  Renormalization factors for local vector and axial vector currents for the
Wilson quark action are perturbatively calculated to one loop order including
finite quark masses from the ratio of the on-shell quark matrix elements in the
Feynman gauge defined on the lattice and in the continuum. For large quark
masses of order unity in lattice units, we find that finite quark mass effects
are quite large: one-loop coefficients of the renormalization factors differ by
100% compared to those in the massless limit.


title:
The Mass Spectrum of Light and Heavy Hadrons from Improved Lattice
  Actions

abstract:
  We use improved lattice actions for glue, light quarks and heavy quarks for
which we use lattice NRQCD to compute hadron masses. Our results are in good
agreement with experiment, except for charmed hadrons. It seems that charmed
quar ks are not well approximated as heavy quarks nor as light quarks.


title:
The Critical Points of Strongly Coupled Lattice QCD at Nonzero Chemical
  Potential

abstract:
  We study QCD at non-zero quark density, zero temperature, infinite coupling
using the Glasgow algorithm. An improved complex zero analysis gives a critical
point \mu_c in agreement with that of chiral symmetry restoration computed with
strong coupling expansions, and monomer-dimer simulations. We observe, however,
two unphysical critical points: the onset for the number density \mu_o, and
\mu_s the saturation threshold, coincident with pathological onsets observed in
past quenched QCD calculations. An analysis of the probability distributions
for particle number supports our physical interpretation of the critical point
\mu_c, and offers a new intepretation of \mu_o, which confirms its unphysical
nature. The perspectives for future lattice QCD calculations of the properties
of dense baryonic matter are briefly discussed.


title: The Spectrum from Lattice NRQCD

abstract:
  I review recent results for heavy-heavy spectroscopy using Lattice NRQCD. The
NRQCD collaboration reports that spin-independent splittings for the $\Upsilon$
are scaling for a sensible range of $\beta$ values in the quenched
approximation. Spin-dependent splittings are not, if the scale is set by
spin-independent splittings. Results which include higher order spin-dependent
relativistic and discretisation corrections show differences from previous
(NRQCD collaboration) results without these. As expected, the differences are
small for $\Upsilon$ but rather large for charmonium. New results from the
SESAM collaboration for $\Upsilon$ spectroscopy on configurations with Wilson
dynamical fermions show good agreement with previous results on HEMCGC
configurations with staggered dynamical fermions.


title: Renormalizability of a lattice chiral fermion in the overlap formulation

abstract:
  Renormalizability of a lattice chiral fermion is studied at one loop level in
the overlap formulation in four dimensions. The fermion chirality is examined
including the self-energy corrections due to gauge interactions. Divergent
terms breaking the chiral symmetry do not appear and the chiral fermion is
renormalized, preserving the correct chiral properties without adding new
counter-terms or tuning the parameters involved. The divergent part of the wave
function renormalization factor agrees with that of the continuum theory. The
overlap formulation of a lattice chiral fermion has passed the important test,
the renormalizability, at one loop level.


title: Phase transitions in abelian lattice gauge theories

abstract:
  We study the phase transition in the abelian lattice gauge theory using the
Wilson-Polyakov line as the order parameter. The Wilson-Polyakov line remains
very small at strong coupling and becomes non-zero at weak coupling, signalling
a confinement to deconfinement phase transition. The decondensation of monopole
loops is responsible for this phase transition. A finite size scaling analysis
of the susceptibility of the Wilson line gives a ratio for $\gamma/\nu$ which
is quite close to the corresponding value in the 3-d planar model. A scaling
behaviour for the monopole loop distribution function is also established at
the point of the second order phase transition. A measurement of the plaquette
susceptibility at the transition point shows that it does not scale with the
four dimensional volume as is expected of a first order bulk transition.


title: Results on Finite Density QCD

abstract:
  A brief summary of the formulation of QCD at finite chemical potental, $\mu$,
is presented. The failure of the quenched approximation to the problem is
reviewed.
  Results are presented for dynamical simulations of the theory at strong and
intermediate couplings. We find that the problems associated with the quenched
theory persist: the onset of non-zero quark number does seem to occur at a
chemical potential $\approx { {m_{\pi}} \over 2}$. However analysis of the
Lee-Yang zeros of the grand canonical partition function in the complex
fugacity plane, ($e^{\mu/T}$), does show signals of critical behaviour in the
expected region of chemical potential.
  Results are presented for a simulation at finite density of the Gross-Neveu
model on a $16^3$ lattice near to the chiral limit. Contrary to our simulations
of QCD no pathologies were found when $\mu$ passed through the value
$m_{\pi}/2}$.


title: Strongly coupled compact lattice QED with staggered fermions

abstract:
  We explore the compact U(1) lattice gauge theory with staggered fermions and
gauge field action -\sum_P [\beta \cos(\Theta_P) + \gamma \cos(2\Theta_P)],
both for dynamical fermions and in the quenched approximation. (\Theta_P
denotes the plaquette angle.) In simulations with dynamical fermions at various
\gamma \le -0.2 on 6^4 lattices we find the energy gap at the phase transition
of a size comparable to the pure gauge theory for \gamma \le 0 on the same
lattice, diminishing with decreasing \gamma. This suggests a second order
transition in the thermodynamic limit of the theory with fermions for \gamma
below some finite negative value. Studying the theory on large lattices at
\gamma = -0.2 in the quenched approximation by means of the equation of state
we find non-Gaussian values of the critical exponents associated with the
chiral condensate, \beta \simeq 0.32 and \delta \simeq 1.8, and determine the
scaling function. Furthermore, we evaluate the meson spectrum and study the
PCAC relation.


title:
$U_A$(1) Anomaly in Background Fields Dominated by QCD-Monopoles on
  SU(2) Lattice

abstract:
  We study $U_A$(1) anomaly of non-perturbative QCD in the maximally abelian
gauge on SU(2) lattice. The existence of the strong correlation between
QCD-monopoles and instantons in the abelian gauge is shown by both analytic and
numerical works including lattice simulations. These results bring us a
conjecture that the $U_A$(1) symmetry would be explicitly broken in the
background fields dominated by QCD-monopoles. We find an evidence for our
conjecture by measuring the chiral-asymmetric zero modes of the Dirac operator
in the backgrounds of QCD-monopoles.


title: Fixed-Point Actions in 1-Loop Perturbation Theory

abstract:
  It has been pointed out in recent papers that the example considered earlier
in the O(N) sigma-model to test whether fixed-point actions are 1-loop perfect
actually checked classical perfection only. To clarify the issue we constructed
the renormalized trajectory explicitly in 1-loop perturbation theory. We found
that the fixed-point action is not exactly 1-loop perfect. The cut-off effects
are, however, strongly reduced also on the 1-loop level relative to those of
the standard and tree level improved Symanzik actions. Some points on off- and
on-shell improvement, Symanzik's program and fixed-point actions are also
discussed.


title: Upsilon Spectrum from NRQCD with Improved Action

abstract:
  We explore the effect of higher order operators in the non-relativistic
formulation of QCD (NRQCD). We calculated masses in the b \bar b spectrum using
quenched gauge configurations at beta = 6.0 and two different NRQCD actions
which have been corrected to order mv^4 and mv^6. The two-point functions are
calculated in a gauge invariant fashion. We find the general structure of the
spectrum to be the same in the two cases. Using the P - 3S1 splitting we
determine the inverse lattice spacings to be 2.44(4) GeV and 2.44(5) GeV for
the mv^4 and mv^6 actions, respectively. We do observe shifts in the spin
splittings. The hyperfine splitting is reduced by approximately 4 MeV, while
the fine splitting is down by up to 10 MeV, albeit with large statistical
errors.


title:
Universality of subleading exponents induced by one dimensional defects
  the case of self-avoiding walks

abstract:
  In this paper we offer some simple and quite general arguments which suggest
that the first subleading exponent $\Delta$ does not depend on the set of
broken symmetries, but only on the dimensionality of the excluded region. An
explicit value for this exponent is conjectured. We reserve analytical and
numerical details to a forthcoming paper.


title:
Universality of subleading corrections for self-avoiding walks in
  presence of one dimensional defects

abstract:
  We study three-dimensional self-avoiding walks in presence of a
one-dimensional excluded region. We show the appearance of a universal
sub-leading exponent which is independent of the particular shape and
symmetries of the excluded region. A classical argument provides the estimate:
$\Delta = 2 \nu - 1 \approx 0.175(1)$. The numerical simulation gives $\Delta =
0.18(2)$.


title: On QCD Thermodynamics with Improved Actions

abstract:
  We discuss recent advances in the calculation of thermodynamic observables
using improved actions. In particular, we discuss the calculation of the
equation of state of the SU(3) gauge theory, the critical temperature in units
of the string tension, the surface tension and the latent heat at the
deconfinement transition. We also present first results from a calculation of
the equation of state for four-flavour QCD using an O(a^2) improved staggered
fermion action and discuss possible further improvements of the staggered
fermion action.


title: Abelian Monopoles in SU(2) Lattice Gauge Theory as Physical Objects

abstract:
  By numerical calculations we show that the abelian monopole currents are
locally correlated with the density of SU(2) lattice action. The correlations
are larger by the order of magnitude in the maximal abelian projection than in
the projections which correspond to the diagonalization of Polyakov line and to
the diagonalization of the plaquette. These facts show that (at least) in the
maximal abelian projection the monopoles are the physical objects, they carry
the SU(2) action. The larger value of \beta, the larger the relative action
carried by monopole. Calculations on the asymmetric lattice show that this
correlation exists also in the deconfinement phase of gluodynamics.


title: f_B with lattice NRQCD including O(1/m_Q^2) corrections

abstract:
  We calculate the heavy-light meson decay constant using lattice NRQCD action
for the heavy quark and Wilson quark action for the light quark over a wide
range in the heavy quark mass. Simulations are carried out on a 16^3 x 32
lattice with 120 quenched gauge configurations generated with the plaquette
action at beta=5.8. For the heavy quark part of the calculation, two sets of
lattice NRQCD action and current operator are employed. The first set includes
terms up to O(1/m_Q) both in the action and the current operator, and the
second set up to O(1/m_Q^2), where m_Q is the bare mass of the heavy quark.
Tree-level values with tadpole improvement are employed for the coefficients in
the expansion. We compare the results obtained from the two sets in detail and
find that the truncation error of higher order relativistic corrections for the
decay constant are adequately small around the mass of the b quark. We also
calculate the 1S hyperfine splitting of B meson, M_{B_s} - M_B and f_{B_s}/f_B
with both sets and find that the 1/m_Q^2 corrections are negligible. Remaining
systematic errors and the limitation of NRQCD theory are discussed.


title: The quantum space-time of c=-2 gravity

abstract:
  We study the fractal structure of space-time of two-dimensional quantum
gravity coupled to c=-2 conformal matter by means of computer simulations. We
find that the intrinsic Hausdorff dimension d_H = 3.58 +/- 0.04. This result
supports the conjecture d_H = -2 \alpha_1/\alpha_{-1}, where \alpha_n is the
gravitational dressing exponent of a spinless primary field of conformal weight
(n+1,n+1), and it disfavours the alternative prediction d_H = 2/|\gamma|. On
the other hand <l^n> ~ r^{2n} for n>1 with good accuracy, i.e. the boundary
length l has an anomalous dimension relative to the area of the surface.


title:
Quantum Fluctuations versus Topology - a Study in U(1)_2 Lattice Gauge
  Theory

abstract:
  Using the geometric definition of the topological charge we decompose the
path integral of 2-dimensional U(1) lattice gauge theory into topological
sectors. In a Monte Carlo simulation we compute the average value of the action
as well as the distribution of its values for each sector separately. These
numbers are compared with analytic lower bounds of the action which are
relevant for classical configurations carrying topological charge. We find that
quantum fluctuations entirely dominate the path integral. Our results for the
probability distribution of the Monte Carlo generated configurations among the
topological sectors can be understood by a semi-phenomenological argument.


title: Is the 2D O(3) Nonlinear $\sigma$ Model Asymptotically Free?

abstract:
  We report the results of a Monte Carlo study of the continuum limit of the
two dimensional O(3) non-linear $\sigma$ model. The notable finding is that it
agrees very well with both the prediction inspired by Zamolodchikovs' S-matrix
ansatz and with the continuum limit of the dodecahedron spin model. The latter
finding renders the existence of asymptotic freedom in the O(3) model rather
unlikely.


title: Remarks on abelian dominance

abstract:
  We used a renormalisation group based smoothing to address two questions
related to abelian dominance. Smoothing drastically reduces short distance
fluctuations but it preserves the long distance physical properties of the
SU(2) configurations. This enabled us to extract the abelian heavy-quark
potential from time-like Wilson loops on Polyakov gauge projected
configurations. We obtained a very small string tension which is inconsistent
with the string tension extracted from Polyakov loop correlators. This shows
that the Polyakov gauge projected abelian configurations do not have a
consistent physical meaning. We also applied the smoothing on SU(2)
configurations to test how sensitive abelian dominance in the maximal abelian
gauge is to the short distance fluctuations. We found that on smoothed SU(2)
configurations the abelian string tension was about 30% smaller than the SU(2)
string tension which was unaffected by smoothing. This suggests that the
approximate abelian dominance found with the Wilson action is probably an
accident and it has no fundamental physical relevance.


title:
On the influence of colour magnetic currents on the confining properties
  of SU(3) lattice gauge theory

abstract:
  We modify the standard Wilson action of SU(3) lattice gauge theory by adding
an extra term which suppresses colour magnetic currents. We present numerical
results of simulations at zero and finite temperature and show that colour
magnetic currents strongly influence the confining properties of SU(3) lattice
gauge theory.


title:
Application of a coordinate space method for the evaluation of lattice
  Feynman diagrams in two dimensions

abstract:
  We apply a new coordinate space method for the evaluation of lattice Feynman
diagrams suggested by L\"uscher and Weisz to field theories in two dimensions.
Our work is to be presented for the theories with massless propagators. The
main idea is to deal with the integrals in position space by making use of the
recursion relation for the free propagator $G(x)$ which allows to compute the
propagator recursively by its values around origin. It turns out that the
method is very efficient and gives very precise results. We illustrate the
technique by evaluating a number of two- and three-loop diagrams explicitly.


title: A New Formulation in Lattice Theory

abstract:
  In this paper we propose a new approach to formulate the field theory on a
lattice. This approach can eliminate the Fermion doubling problem, preserve the
chiral symmetry and get the same dispersion relation for both Fermion and Boson
fields. This gives us the possibility to write down the chiral model (such as
the Weinberg-Salam model) on a lattice.


title: Topology at zero and finite T in SU(2) Yang-Mills theory

abstract:
  We determine the topological susceptibility \chi at T=0 and its behaviour at
finite T across the deconfining transition in pure SU(2) gauge theory. We use
an improved topological charge density operator. \chi goes to zero above T_c,
but more slowly than in SU(3) gauge theory.


title: Recent Advances in Hamiltonian Lattice Gauge Theory

abstract:
  We review the recent advances in the Hamiltonian formulation of lattice gauge
theory for approaching the continuum physics. In particular, vacuum wave
function and glueball spectrum calculations by coupled cluster method with
truncation scheme preserving the continuum behavior are described.


title: Fixed Point Four-Fermi Theories

abstract:
  I review dynamical chiral symmetry breaking in four-fermi models, including
results of Monte Carlo simulations with dynamical fermions. For 2<d<4, where
the phase transition defines an ultraviolet fixed point of the renormalisation
group, the continuum theory may either be describable using the large-N_f
expansion, as in the case of the Gross-Neveu model, or be intrinsically
non-perturbative, as in the case of the Thirring model. For d=4, the models are
trivial and are described by a mean field equation of state with logarithmic
corrections to scaling, which may nonetheless define new universality classes
distinct from those of ferromagnetism.


title: Properties of Renormalization Group Transformations

abstract:
  We describe some properties of Renormalization Group transformations.
Especially we show why some of the RG transformations have redundant
eigenoperators with eigenvalues that cannot be determined by simple dimensional
analysis and give the corresponding formulae.


title: On the SU(2)-Higgs Phase Transition

abstract:
  The properties of the Confinement-Higgs phase transition in the SU(2)-Higgs
model with fixed modulus are investigated. We show that the system exhibits a
transient behavior up to L=24 along which the order of the phase transition
cannot be discerned. To get stronger conclusions about this point, without
going to prohibitive large lattice sizes, we have introduced a second
(next-to-nearest neighbors) gauge-Higgs coupling, k2. On this extended
parameter space we find a line of phase transitions which become increasely
weaker as k2 tends to 0. The results point to a first order character for the
transition with the standard action (k2 = 0).


title: A Wilson-Yukawa model with undoubled chiral fermions in 2D

abstract:
  We consider the fermion spectrum in the strong coupling vortex phase of a
lattice fermion-scalar model with a global $U(1)_L\times U(1)_R$, in 2D, in the
context of a recently proposed two-cutoff lattice formulation. The fermion
doublers are made massive by a strong Wilson-Yukawa coupling, but in contrast
with the standard formulation of these models, in which the light fermion
spectrum was found to be massive and vectorlike, we find massless undoubled
fermions with chiral quantum numbers at finite lattice spacing. When the global
symmetry is gauged, this model is expected to give rise to a chiral gauge
theory.


title: Further discussions on a possible lattice chiral gauge theory

abstract:
  In a possible $SU_L(2)$ lattice chiral gauge theory with a large multifermion
coupling, we try to further clarify the threshold phenomenon: the possibility
that the right-handed three-fermion state turns into the virtual states of its
constituents (free chiral fermions) in the low-energy limit. Provided this
phenomenon occurs, we discuss the chiral gauge coupling, Ward identities and
the gauge anomaly within the gauge-invariant prescription of the perturbative
chiral gauge theory.


title: Domain wall quarks and kaon weak matrix elements

abstract:
  We present lattice calculations of kaon matrix elements with domain wall
fermions. Using lattices with beta=5.85, 6.0, and 6.3, we estimate B_K(approx 2
GeV)=0.628(47) in quenched QCD which is consistent with previous calculations.
At beta=6.0 and 5.85 we find the ratio f_K/m_rho in agreement with the
experimental value, within errors. These results support expectations that O(a)
errors are exponentially suppressed in low energy (E<< a^{-1}) observables, and
indicate that domain wall fermions have good scaling behavior at relatively
strong couplings. We also demonstrate that the axial current numerically
satisfies the lattice analog of the usual continuum axial Ward identity.


title: Pad\'e - Z$_2$ Estimator of Determinants

abstract:
  We introduce the Pad\'e--Z$_2$ (PZ) stochastic estimator for calculating
determinants and determinant ratios. The estimator is applied to the
calculation of fermion determinants from the two ends of the Hybrid Monte Carlo
trajectories with pseudofermions. Our results on the $8^3 \times 12$ lattice
with Wilson action show that the statistical errors from the stochastic
estimator can be reduced by more than an order of magnitude by employing an
unbiased variational subtraction scheme which utilizes the off-diagonal
matrices from the hopping expansion. Having been able to reduce the error of
the determinant ratios to about 20 % with a relatively small number of noise
vectors, this may become a feasible algorithm for simulating dynamical fermions
in full QCD. We also discuss the application to the density of states in
Hamiltonian systems.


title:
Chiral transition and monopole percolation in lattice scalar QED with
  quenched fermions

abstract:
  We study the interplay between topological observables and chiral and Higgs
transitions in lattice scalar QED with quenched fermions. Emphasis is put on
the chiral transition line and magnetic monopole percolation at strong gauge
coupling. We confirm that at infinite gauge coupling the chiral transition is
described by mean field exponents. We find a rich and complicated behaviour at
the endpoint of the Higgs transition line which hampers a satisfactory analysis
of the chiral transition. We study in detail an intermediate coupling, where
the data are consistent both with a trivial chiral transition clearly separated
from monopole percolation and with a chiral transition coincident with monopole
percolation, and characterized by the same critical exponent $\nu \simeq 0.65$.
We discuss the relevance (or lack thereof) of these quenched results to our
understanding of the \chupiv\ model. We comment on the interplay of magnetic
monopoles and fermion dynamics in more general contexts.


title: A disorder parameter for dual superconductivity in gauge theories

abstract:
  A detailed discussion is given of the disorder parameter for dual
superconductivity of lattice gauge theories, introduced in a previous paper,
and of its relation to other approaches. New lattice data are reported. Among
other results, we find that the dual superconductivity of compact U(1) is type
II.


title: SESAM and TXL Results for Wilson Action--A Status Report

abstract:
  Results from two studies of full QCD with two flavours of dynamical Wilson
fermions are presented. At beta=5.6, the region 0.83 > m_pi/m_rho > 0.56 at
m_pia > 0.23 L^{-1} is explored. The SESAM collaboration has generated
ensembles of about 200 statistically independent configurations on a 16^3 x
32-lattice at three different kappa-values and is entering the final phase of
data analysis. The TXL simulation on a 24^3 x 40-lattice at two kappa-values
has reached half statistics and data analysis has started recently, hence most
results presented here are preliminary. The focus of this report is fourfold:
we demonstrate that algorithmic improvements like fast Krylov solvers and
parallel preconditioning recently introduced can be put into practise in full
QCD simulations, we present encouraging observations as to the critical
dynamics of the Hybrid Monte Carlo algorithm in the approach to the chiral
limit, we mention signal improvements of noisy estimator techniques for
disconnected diagrams to the pi-N sigma term, and we report on SESAM's results
for light hadron spectrum, light quark masses, and heavy quarkonia.


title: Quadratically optimized polynomials for fermion simulations

abstract:
  Quadratically optimized polynomials are described which are useful in
multi-bosonic algorithms for Monte Carlo simulations of quantum field theories
with fermions. Algorithms for the computation of the coefficients and roots of
these polynomials are described and their implementation in the algebraic
manipulation language Maple is discussed. Tests of the evaluation of
polynomials on dynamical fermion configurations are performed. In a simple
special case the obtained polynomial approximations are compared to Chebyshev
polynomials.


title: Staggered fermion matrix elements using smeared operators

abstract:
  We investigate the use of two kinds of staggered fermion operators, smeared
and unsmeared. The smeared operators extend over a $4^4$ hypercube, and tend to
have smaller perturbative corrections than the corresponding unsmeared
operators. We use these operators to calculate kaon weak matrix elements on
quenched ensembles at $\beta=6.0$, 6.2 and 6.4. Extrapolating to the continuum
limit, we find $B_K(NDR, 2 GeV)= 0.62\pm 0.02(stat)\pm 0.02(syst)$. The
systematic error is dominated by the uncertainty in the matching between
lattice and continuum operators due to the truncation of perturbation theory at
one-loop. We do not include any estimate of the errors due to quenching or to
the use of degenerate $s$ and $d$ quarks. For the $\Delta I = {3/2}$
electromagnetic penguin operators we find $B_7^{(3/2)} = 0.62\pm 0.03\pm 0.06$
and $B_8^{(3/2)} = 0.77\pm 0.04\pm 0.04$. We also use the ratio of unsmeared to
smeared operators to make a partially non-perturbative estimate of the
renormalization of the quark mass for staggered fermions. We find that tadpole
improved perturbation theory works well if the coupling is chosen to be
$\alpha_\MSbar(q^*=1/a)$.


title: The Rome Approach to Chirality

abstract:
  Some general considerations on the problem of non perturbative definition of
Chiral Gauge Theories are presented and exemplified within the particular
proposal known as the Rome Approach.


title: Exotic mesons in quenched lattice QCD

abstract:
  Since gluons in QCD are interacting fundamental constituents just as quarks
are, we expect that in addition to mesons made from a quark and an antiquark,
there should also be glueballs and hybrids (bound states of quarks, antiquarks
and gluons). In general, these states would mix strongly with the conventional
q-bar-q mesons. However, they can also have exotic quantum numbers inaccessible
to q-bar-q mesons. Confirmation of such states would give information on the
role of "dynamical" color in low energy QCD. In the quenched approximation we
present a lattice calculation of the masses of mesons with exotic quantum
numbers. These hybrid mesons can mix with four quark (q-bar-q-bar-q-q) states.
The quenched approximation partially suppresses this mixing. Nonetheless, our
hybrid interpolating fields also couple to four quark states. Using a four
quark source operator, we demonstrate this mixing for the 1-+ meson. Using the
conventional Wilson quark action, we calculate both at reasonably light quark
masses, intending to extrapolate to small quark mass, and near the charmed
quark mass, where we calculate the masses of some c-bar-c-g hybrid mesons. The
hybrid meson masses are large --- over 4 GeV for charmonium and more than twice
the vector meson mass at our smallest quark mass, which is near the strange
quark mass.


title: New lattice approaches to the $\Delta I=1/2$ rule

abstract:
  Lattice QCD should allow a derivation of the $\Delta I=1/2$ rule from first
principles, but numerical calculations to date have been plagued by a variety
of problems. After a brief review of these problems, we present several new
methods for calculating $K\to\pi\pi$ amplitudes. These are designed for Wilson
fermions, though they can be used also with staggered fermions. They all
involve a non-perturbative determination of matching coefficients. We show how
problems of operator mixing can be greatly reduced by using point-split
hadronic currents, and how CP violating parts of the $K\to\pi\pi$ amplitudes
can be calculated by introducing a fake top quark. Many of the methods can also
be applied to the calculation of two body non-leptonic B-meson decays.


title:
Gauge Freedom in Chiral Gauge Theory with Vacuum Overlap --
  Four-dimensional case

abstract:
  Dynamical nature of the gauge degree of freedom and its effect to fermion
spectrum are studied for four-dimensional nonabelian chiral gauge theory in the
vacuum overlap formulation. The covariant gauge fixing term and the
Faddeev-Popov determinant are introduced by hand as a weight for the gauge
average. At $\beta=\infty$, as noticed by Hata some time ago, the model is
renormalizable at one-loop and the gauge fixing term turns into an
asymptotically free self-coupling of the gauge freedom, even in the presence of
the gauge symmetry breaking of the complex phase of chiral determinant. The
severe infrared divergence occurs in the perturbation expansion and it prevents
local order parameters from emerging. The Foerster-Nielsen-Ninomiya mechanism
works in this perturbative framework: the small explicit gauge symmetry
breaking term does not affect the above infrared structure. Based on these
dynamical features, which is quite similar to the two-dimensional nonlinear
sigma model, we assume that the global gauge symmetry does not break
spontaneously and the gauge freedom acquires mass dynamically. The asymptotic
freedom allows us to tame the gauge fluctuation by approaching the critical
point of the gauge freedom without spoiling its disordered nature. Then it is
argued that the disordered gauge freedom does not necessarily cause the
massless chiral state in the (waveguide) boundary correlation function and that
the entire fermion spectrum can be chiral.


title:
Topological Charge and the Spectrum of the Fermion Matrix in
  Lattice-QED_2

abstract:
  We investigate the interplay between topological charge and the spectrum of
the fermion matrix in lattice-QED_2 using analytic methods and Monte Carlo
simulations with dynamical fermions. A new theorem on the spectral
decomposition of the fermion matrix establishes that its real eigenvalues (and
corresponding eigenvectors) play a role similar to the zero eigenvalues (zero
modes) of the Dirac operator in continuous background fields. Using numerical
techniques we concentrate on studying the real part of the spectrum. These
results provide new insights into the behaviour of physical quantities as a
function of the topological charge. In particular we discuss fermion
determinant, effective action and pseudoscalar densities.


title: Heavy Quarkonia at High Temperature

abstract:
  We present a new method to study the properties of heavy quarks at finite
temperature. It combines non-relativistic QCD with an improved gluonic action
on anisotropic lattices. The efficiency of the approach is demonstrated by the
first non-perturbative calculation of the temperature dependence of low-lying
quarkonium "pole" masses. For ground state meson masses in the region between
charmonium and bottomonium we find only very little variation up to our highest
temperature which corresponds to T approximately 1.2 Tc while first excited
states indicate a large mass shift.


title: Heavy-light decay constants---MILC results with the Wilson action

abstract:
  We present the current status of our ongoing calculations of pseudoscalar
meson decay constants for mesons that contain one light and one heavy quark
(f_B, f_{B_s}, f_D, f_{D_s}). We are currently generating new gauge
configurations that include dynamical quarks and calculating the decay
constants. In addition, we have several new results for the static
approximation. Those results, as well as several refinements to the analysis,
are new since Lattice '96. Our current (still preliminary) value for f_B is 156
+- 11 +- 30 +- 14 MeV, where the first error is from statistical and fitting
errors, the second error is an estimate of other systematic errors within the
quenched approximation and the third error is an estimate of the quenching
error. For the ratio f_{B_s}/f_B, we get 1.11 +- 0.02 +- 0.03 +- 0.07.


title:
Light hadron spectrum---MILC results with the Kogut-Susskind and Wilson
  actions

abstract:
  We present the current status of our ongoing calculations of the light hadron
spectrum with both Kogut-Susskind (KS) and Wilson quarks in the valence or
quenched approximation. We discuss KS quarks first and find that the chiral
extrapolation is potentially the biggest source of systematic error. For the
Wilson case, we focus on finite volume and source size effects at 6/g^2=5.7. We
find no evidence to support the claim that there is a finite volume effect
between N_s=16 and 24 of approximately 5%.


title: Two-Cutoff Lattice Regularization of Chiral Gauge Theories

abstract:
  I review our method to formulate chiral gauge theories on the lattice based
on a two-cutoff lattice regularization, and discuss recent numerical results in
a chiral U(1) gauge theory in 2D.


title: Overlap in odd dimensions

abstract:
  In odd dimensions the lattice overlap formalism is simpler than in even
dimensions. Masslessness of fermions can still be preserved without fine tuning
and gauge invariance without gauge averaging can be maintained, although,
sometimes, only at the expense of parity invariance. When parity invariance is
enforced invariance under small gauge transformations can be maintained and
continuum global gauge anomalies are reproduced.


title:
The four dimensional site-diluted Ising model: a finite-size scaling
  study

abstract:
  Using finite-size scaling techniques, we study the critical properties of the
site-diluted Ising model in four dimensions. We carry out a high statistics
Monte Carlo simulation for several values of the dilution. The results support
the perturbative scenario: there is only the Ising fixed point with large
logarithmic scaling corrections. We obtain, using the Perturbative
Renormalization Group, functional forms for the scaling of several observables
that are in agreement with the numerical data.


title: Enhanced chiral logarithms in partially quenched QCD

abstract:
  I discuss the properties of pions in ``partially quenched'' theories, i.e.
those in which the valence and sea quark masses, $m_V$ and $m_S$, are
different. I point out that for lattice fermions which retain some chiral
symmetry on the lattice, e.g. staggered fermions, the leading order prediction
of the chiral expansion is that the mass of the pion depends only on $m_V$, and
is independent of $m_S$. This surprising result is shown to receive corrections
from loop effects which are of relative size $m_S \ln m_V$, and which thus
diverge when the valence quark mass vanishes. Using partially quenched chiral
perturbation theory, I calculate the full one-loop correction to the mass and
decay constant of pions composed of two non-degenerate quarks, and suggest
various combinations for which the prediction is independent of the unknown
coefficients of the analytic terms in the chiral Lagrangian. These results can
also be tested with Wilson fermions if one uses a non-perturbative definition
of the quark mass.


title: Phase Structure of Lattice QCD for General Number of Flavors

abstract:
  We investigate the phase structure of lattice QCD for general number of
flavors $N_F$. Based on numerical results combined with the result of the
perturbation theory we propose the following picture: When $N_F \ge 17$, there
is only a trivial fixed point and therefore the theory in the continuum limit
is trivial. On the other hand, when $16 \ge N_F \ge 7$, there is a non-trivial
fixed point and therefore the theory is non-trivial with anomalous dimensions,
however, without quark confinement. Theories which satisfy both quark
confinement and spontaneous chiral symmetry breaking in the continuum limit
exist only for $N_F \le 6$.


title: Phase Structure of Lattice QCD with Wilson fermion at Finite Temperature

abstract:
  We review our attempt at understanding the phase structure of lattice QCD
with the Wilson fermion formulation at finite temperature, based on a
spontaneous breakdown of parity-flavor symmetry. Numerical results
demonstrating explicitly the spontaneous breakdown of parity-flavor symmetry
beyond the critical line at both zero and finite temperatures are reported. The
phase structure and order of the chiral transition are reported for $N_f=2$,3,
and 4 flavors, and the approach towards the continuum limit is discussed.


title:
Scaling of Non-Perturbatively O(a) Improved Wilson Fermions: Hadron
  Spectrum, Quark Masses and Decay Constants

abstract:
  We compute the hadron mass spectrum, the quark masses and the meson decay
constants in quenched lattice QCD with non-perturbatively $O(a)$ improved
Wilson fermions. The calculations are done for two values of the coupling
constant, $\beta = 6.0$ and 6.2, and the results are compared with the
predictions of ordinary Wilson fermions. We find that the improved action
reduces lattice artifacts as expected.


title: Exactly massless quarks on the lattice

abstract:
  It is suggested that the fermion determinant for a vector-like gauge theory
with strictly massless quarks can be represented on the lattice as
$\det{{1+V}\over 2}$, where $V=X(X^\dagger X)^{-1/2}$ and $X$ is the
Wilson-Dirac lattice operator with a negative mass term. There is no undesired
doubling and no need for any fine tuning. Several other appealing features of
the formula are pointed out.


title:
String Tension and Thermodynamics with Tree Level and Tadpole Improved
  Actions

abstract:
  We calculate the string tension, deconfinement transition temperature and
bulk thermodynamic quantities of the SU(3) gauge theory using tree level and
tadpole improved actions. Finite temperature calculations have been performed
on lattices with temporal extent N_tau = 3 and 4. Compared to calculations with
the standard Wilson action on this size lattices we observe a drastic reduction
of the cut-off dependence of bulk thermodynamic observables at high
temperatures. In order to test the influence of improvement on long-distance
observables at T_c we determine the ratio T_c/sqrt(sigma). For all actions,
including the standard Wilson action, we find results which differ only little
from each other. We do, however, observe an improved asymptotic scaling
behaviour for the tadpole improved action compared to the Wilson and tree level
improved actions.


title: Fixed point action for the massless lattice Schwinger model

abstract:
  We determine non-perturbatively the fixed-point action for fermions in the
two-dimensional U(1) gauge (Schwinger) model. This is done by iterating a block
spin transformation in the background of non-compact gauge field configurations
sampled according to the (perfect) Gaussian measure. The resulting action has
123 independent couplings, is bilinear in the Grassmann fields, gauge-invariant
by considered the compact gauge transporters and localized within a $7\times 7$
lattice centered around one of the fermions. We then simulate the model at
various values of $\beta$ and compare with results obtained with the Wilson
fermion action. We find excellent improvement for the studied observables
(propagators and masses).


title: Improved Renormalization of Lattice Operators: A Critical Reappraisal

abstract:
  We systematically examine various proposals which aim at increasing the
accuracy in the determination of the renormalization of two-fermion lattice
operators. We concentrate on three finite quantities which are particularly
suitable for our study: the renormalization constants of the vector and axial
currents and the ratio of the renormalization constants of the scalar and
pseudoscalar densities. We calculate these quantities in boosted perturbation
theory, with several running boosted couplings, at the "optimal" scale q*. We
find that the results of boosted perturbation theory are usually (but not
always) in better agreement with non-perturbative determinations of the
renormalization constants than those obtained with standard perturbation
theory. The finite renormalization constants of two-fermion lattice operators
are also obtained non-perturbatively, using Ward Identities, both with the
Wilson and the tree-level Clover improved actions, at fixed cutoff ($\beta$=6.4
and 6.0 respectively). In order to amplify finite cutoff effects, the quark
masses (in lattice units) are varied in a large interval 0<am<1. We find that
discretization effects are always large with the Wilson action, despite our
relatively small value of the lattice spacing ($a^{-1} \simeq 3.7$ GeV). With
the Clover action discretization errors are significantly reduced at small
quark mass, even though our lattice spacing is larger ($a^{-1} \simeq 2$ GeV).
However, these errors remain substantial in the heavy quark region. We have
implemented a proposal for reducing O(am) effects, which consists in matching
the lattice quantities to their continuum counterparts in the free theory. We
find that this approach still leaves appreciable, mass dependent,
discretization effects.


title: Perturbative Improvement for Lattice QCD: An Update

abstract:
  Recent developments in the Symanzik improvement program for lattice QCD are
reviewed.


title:
Dynamical Gauge Symmetry Breaking and Superconductivity in
  three-dimensional systems

abstract:
  We discuss dynamical breaking of non-abelian gauge groups in three
dimensional (lattice) gauge systems via the formation of fermion condensates. A
physically relevant example, motivated by condensed-matter physics, is that of
a fermionic gauge theory with group $SU(2)\otimes U_S(1) \otimes U_{E}(1)$. In
the strong U_S(1) region, the SU(2) symmetry breaks down to a U(1), due to the
formation of a parity-invariant fermion condensate. We conjecture a phase
diagram for the theory involving a critical line, which separates the regions
of broken SU(2) symmetry from those where the symmetry is restored. In the
broken phase, the effective Abelian gauge theory is closely related to an
earlier model of two-dimensional parity-invariant superconductivity in doped
antiferromagnets. The superconductivity in the model occurs in the
Kosterlitz-Thouless mode, since strong phase fluctuations prevent the existence
of a local order parameter. Some physical consequences of the $SU(2) \times
U_S(1)$ phase diagram for the (doping-dependent) parameter space of this
condensed-matter model are briefly discussed.


title: Collapse of 4D random geometries

abstract:
  We extend the analysis of the Backgammon model to an ensemble with a fixed
number of balls and a fluctuating number of boxes. In this ensemble the model
exhibits a first order phase transition analogous to the one in higher
dimensional simplicial gravity. The transition relies on a kinematic
condensation and reflects a crisis of the integration measure which is probably
a part of the more general problem with the measure for functional integration
over higher (d>2) dimensional Riemannian structures.


title:
A lattice Monte Carlo study of Inverse Symmetry Breaking in a two-scalar
  model in three dimensions

abstract:
  We carry a Monte Carlo study of the coupled two-scalar $\lambda\phi^2_1
\phi^2_2$ model in three dimensions. We find no trace of Inverse Symmetry
Breaking in the region of negative $\lambda$'s for which the one-loop effective
potential predicts this phenomenon. Moreover, for $\lambda$'s negative enough,
but still in the stability region for the potential, one of the transitions
turns out to be of first order, both for zero and finite temperature.


title: Antiferromagnetic O(N) models in four dimensions

abstract:
  We study the antiferromagnetic O(N) model in the F_4 lattice. Monte Carlo
simulations are applied for investigating the behavior of the transition for
N=2,3. The numerical results show a first order nature but with a large
correlation length. The $N \to \infty$ limit is also considered with analytical
methods.


title: The Ising model and bubbles in the quark-gluon plasma

abstract:
  I review evidence for the stability of bubbles in the quark-gluon plasma near
the confinement phase transition. In analogy with the much-studied oil-water
emulsions, this raises the possibility that there are many phases between the
pure plasma and the pure hadron gas, characterized by spontaneous inhomogeneity
and modulation. In studying emulsions, statistical physicists have reproduced
many of their phases with microscopic models based on Ising-like theories with
competing interactions. Hence we seek an effective Ising Hamiltonian for the
SU(3) gauge theory near its transition.


title:
Weak coupling expansion of a chiral gauge theory on a lattice in the
  overlap formulation

abstract:
  Weak coupling expansion of a chiral gauge theory on a lattice is discussed in
the overlap formulation. We analyze the fermion propagator and the
fermion-fermion-gauge boson vertex in the one loop level. The chiral properties
of the propagator and vertex are correctly preserved without tuning the
parameters involved even after the one-loop renormalization, and the
ultraviolet divergent parts agree with the continuum theory. Our analysis,
together with the existing studies on the vacuum polarization and the gauge
boson n-point functions, completes the proof of the renormalizability of this
formulation to the one loop level.


title: Phase Diagram of 3d U(1)+Higgs Theory

abstract:
  We study the properties of the phase transition in three dimensional
U(1)+Higgs theory or Ginzburg-Landau model of superconductivity. Special
attention is paid to large values of scalar self coupling (Type II
superconductors), where the nature of the transition is unclear. We present
some evidence for an unusual transition in this regime.


title:
Dimensional Reduction and Hot QCD: Calculating the Debye Mass
  Non-Perturbatively

abstract:
  We study the phase diagram of the 3-dimensional SU(2) + adjoint Higgs theory,
and investigate to what extent it can be used as an effective theory of the
4-dimensional high-T SU(2) QCD. The relation between the parameters in 4 and 3
dimensions is obtained through dimensional reduction. The high-T (deconfined)
QCD phase corresponds to the symmetric phase of the 3-D Higgs theory. In the
relevant parameter region the symmetric phase is not stable, but the
metastability is strong enough to make precise measurements possible. In
particular, we measure the Debye mass using a gauge invariant operator.


title: Chiral Gauge Theories in the Overlap Formalism

abstract:
  The overlap formula for the chiral determinant is presented and the
realization of gauge anomalies and gauge field toplogy in this context is
discussed. The ability of the overlap formalism to deal with supersymmetric
theories and Majorana-Weyl fermions is outlined. Two applications of the
overlap formalism are discussed in some detail. One application is the
computation of a fermion number violating process in a two dimensional U(1)
chiral gauge theory. The second application is a measurement of the probability
ditribution of the index of the chiral Dirac operator in four dimensional pure
SU(2) lattice gauge theory.


title: Simulations of the electroweak plasma at finite temperature

abstract:
  We investigate the SU(2) Higgs model at a Higgs Boson mass of \simeq 34 GeV
for temperatures at the electroweak scale. We discuss in detail the critical
temperature, the scalar field vacuum expectation value and the latent heat. We
also consider for which temperatures the plasma can be regarded as radiation
dominated.


title: The Phase Transition in SU(2)-Higgs

abstract:
  We investigate the properties of the Confinement-Higgs phase transition in
the SU(2)-Higgs model. The system is shown to exhibit a transient behavior up
to L=24 along which, the order of the phase transition cannot be discerned. In
order to get a global vision on the problem, we have introduced a second
(next-to-nearest neighbors) gauge-Higgs coupling (k2). On this extended
parameter space we find a line of phase transitions becoming increasely weak as
the standard case is approached (k2 = 0). From the global behavior on this
parameter space we conclude that the transition is also first order in the
standard case.


title: Algorithmic aspects of multicanonical simulations

abstract:
  Monte Carlo (MC) simulations of many systems, in particular those with
conflicting constraints, can be considerably speeded up by using multicanonical
or related methods. Some of these approaches sample with a-priori unknown
weight factors. After introducing the concept, I shall focus on two aspects:
(i) Opinions about the optimal choice of weight factors. (ii) Methods to get
weight factor estimates, with emphasize on a multicanonical recursion.


title: Approximate actions for dynamical fermions

abstract:
  Recent developments and applications of approximate actions for full lattice
QCD are described. We present first results based on the stochastic estimation
of the fermion determinant on $12^3\times 24$ configurations at $\beta=5.2$.


title: Quenched Chiral Perturbation Theory to one loop

abstract:
  We calculate the divergences of the generating functional of quenched Chiral
Perturbation Theory at one loop, and renormalize the theory by an appropriate
definition of the counterterms. We show that the quenched chiral logarithms can
be reabsorbed in the renormalization of the B_0 parameter which, at lowest
order, is proportional to the vacuum expectation value of the scalar quark
density. Finally, we calculate several quantities at one loop to analyze the
modifications induced by quenching in the finite part of the one-loop
corrections. We point out that some of the finite loop corrections may diverge
in the chiral limit.


title: Quenched Spectroscopy for the N=1 Super-Yang-Mills Theory

abstract:
  We present results for the Quenched SU(2) N=1 Super-Yang-Mills spectrum at
$\beta=2.6$, on a $V=16^3 \times 32$ lattice, in the OZI approximation. This is
a first step towards the understanding of the chiral limit of lattice N=1 SUSY.


title:
Mathematical Derivation of Chiral Anomaly in Lattice Gauge Theory with
  Wilson's Action

abstract:
  Chiral U(1) anomaly is derived with mathematical rigor for a Euclidean
fermion coupled to a smooth external U(1) gauge field on an even dimensional
torus as a continuum limit of lattice regularized fermion field theory with the
Wilson term in the action. The present work rigorously proves for the first
time that the Wilson term correctly reproduces the chiral anomaly.


title:
Lattice-Constrained Parametrizations of Form Factors for Semileptonic
  and Rare Radiative B Decays

abstract:
  We describe the form factors for B to rho lepton neutrino and B to K* gamma
decays with just two parameters and the two form factors for B to pi lepton
neutrino with a further two or three parameters. The parametrizations are
consistent with heavy quark symmetry, kinematic constraints and lattice
results, which we use to determine the parameters. In addition, we test
versions of the parametrizations consistent (or not) with light-cone sum rule
scaling relations at q^2=0.


title: Screening Lengths in SU(2) Gauge Theory at Finite Temperature

abstract:
  We discuss the calculation of electric and magnetic screening masses in SU(2)
gauge theory. The temperature dependence of these masses obtained from the
long-distance behaviour of spatial correlation functions has been analyzed for
temperatures up to 10000 T_c.


title:
Scaling Analysis of Chiral Phase Transition for Two Flavors of
  Kogut-Susskind Quarks

abstract:
  Report is made of a systematic scaling study of the finite-temperature chiral
phase transition of two-flavor QCD with the Kogut-Susskind quark action based
on simulations on $L^3\times4$ ($L$=8, 12 and 16) lattices at the quark mass of
$m_q=0.075, 0.0375, 0.02$ and 0.01. Our finite-size data show that a phase
transition is absent for $m_q\geq 0.02$, and quite likely also at $m_q=0.01$.
The scaling behavior of susceptibilities as a function of $m_q$ is consistent
with a second-order transition at $m_q=0$. However, the exponents deviate from
the O(2) or O(4) values theoretically expected.


title: Study of the Coulomb-Higgs transition in the Abelian Higgs Model

abstract:
  The order of the Coulomb-Higgs transition in the U(1)-Higgs model with
unfrozen modulus of the scalar field is studied. Large lattices (up to $24^4$
in one case) and high statistics are used. We fix $\beta =1.15$ and explore
specially a region of $\lambda$-values where metastability is observed. We
study the thermodynamical limit of several observables, in particular, the
latent heat, the specific heat, the decrement of the free energy between the
maxima and the central minimum of the two-peaked histogram, the Binder cumulant
and the displacement of the critical coupling with the lattice size. The
results point towards a second order transition for $\lambda \gtrsim 0.005$,
while for smaller values of $\lambda$ the strong metastability growing with the
lattice size seems to derive from a first order character.


title: Flux-tube Structure, Sum Rules and Beta-functions in SU(2)

abstract:
  Action and energy flux-tube profiles are computed, in SU(2) with
beta=2.4,2.5, for two quarks up to 1 fm apart and for which the colour fields
are in their ground state (A_1g) and the first (E_u) and higher (A'_1g) excited
gluonic states. When these profiles are integrated over all space, a scaling
comparison is made between the beta=2.4 and 2.5 data. Using sum rules, these
integrated forms also permit an estimate to be made of generalised
beta-functions giving b(2.4)=-0.312(15), b(2.5)=-0.323(9), f(2.4)=0.65(1) and
f(2.5)=0.68(1). When the profiles are integrated only over planes transverse to
the interquark line and assuming underlying string features, scaling
comparisons are again made near the centres of the interquark line for the
largest interquark distances. For the A'_{1g} case, some of the profiles
exhibit a 'dip-like' structure characteristic of the Isgur-Paton model.


title: Hybrid and Orbitally Excited Mesons in Quenched QCD

abstract:
  We use lattice methods to evaluate from first principles the spectrum of
hybrid mesons produced by gluonic excitations in quenched QCD with quark masses
near the strange quark mass. For the spin-exotic mesons with $J^{PC}=1^{-+},\
0^{+-}$, and $2^{+-}$ which are not present in the quark model, we determine
the lightest state to be $1^{-+}$ with mass of 2.0(2) GeV. Results obtained for
orbitally excited mesons are also presented.


title: Complex zeros of the 2d Ising model on dynamical random lattices

abstract:
  We study the zeros in the complex plane of the partition function for the
Ising model coupled to $2d$ quantum gravity for complex magnetic field and for
complex temperature. We compute the zeros by using the exact solution coming
from a two matrix model and by Monte Carlo simulations of Ising spins on
dynamical triangulations. We present evidence that the zeros form simple
one-dimensional patterns in the complex plane, and that the critical behaviour
of the system is governed by the scaling of the distribution of singularities
near the critical point.


title: Full QCD simulation on CP-PACS

abstract:
  A status report is made of an on-going full QCD study on the CP-PACS aiming
at a comparative analysis of the effects of improving gauge and quark actions
on hadronic quantities and static quark potential. Simulations are made for
four action combinations, the plaquette or an RG-improved action for gluons and
the Wilson or SW-clover action for quarks, at $a^{-1} \approx 1.1$-1.3GeV and
$m_\pi/m_\rho \approx 0.7$-0.9. Results demonstrate clearly that the clover
term markedly reduces discretization errors for hadron spectrum, while adding
six-link terms to the plaquette action leads to much better rotational symmetry
in the potential. These results extend experience with quenched simulations to
full QCD.


title: Phase Diagram of SO(3) Lattice Gauge Theory at Finite Temperature

abstract:
  The phase diagram of SO(3) lattice gauge theory at finite temperature is
investigated by Monte Carlo techniques with a view i) to understand the
relationship between the deconfinement phase transitions in the SU(2) and SO(3)
lattice gauge theories and ii) to resolve the current ambiguity of the nature
of the high temperature phases of the latter. Phases with positive and negative
adjoint Polyakov loop are shown to have the same physics. A first order
deconfining phase transition is found for N_t=4.


title:
Liapunov Exponents and the Reversibility of Molecular Dynamics
  Algorithms

abstract:
  We study the phenomenon of lack of reversibility in molecular dynamics
algorithms for the case of Wilson's lattice QCD. We demonstrate that the
classical equations of motion that are employed in these algorithms are chaotic
in nature. The leading Liapunov exponent is determined in a range of coupling
parameters. We give a quantitative estimate of the consequences of the
breakdown of reversibility due to round-off errors.


title: Multi-boson simulation of the Schroedinger functional

abstract:
  We discuss the choice of parameters and report some results for unquenched
simulations of the Schroedinger functional with a non-hermitean variant of
Luescher's multi-boson algorithm.


title: On the Phase Diagram of a Lattice U(1) Gauge Theory with Gauge Fixing

abstract:
  As a first step towards a nonperturbative investigation of the gauge-fixing
(Rome) approach to lattice chiral gauge theories we study a U(1) model with an
action that includes a local gauge-fixing term and a mass counterterm for the
gauge fields. The model is studied on the trivial orbit so that only the
dynamics of the longitudinal gauge degrees of freedom is taken into account.
The phase diagram of this higher-derivative scalar field theory is determined,
both in the mean-field approximation and numerically. The continuum limit of
the model corresponds to a continuous phase transition between a ferromagnetic
(FM) phase where the global U(1) symmetry is broken, and a so-called helicoidal
ferromagnetic (FMD) phase with broken U(1) symmetry and a nonvanishing
condensate of the vector field. The global U(1) symmetry is restored in this
continuum limit. We show that our data for the magnetization in the FM and FMD
phases are in good agreement with perturbation theory.


title: Is the doubler of the electron an antiquark?

abstract:
  Reassigning degrees of freedom in the standard model allows an interpretation
where the SU(2) gauge group is vector-like and parity violation moves to the
strong and electromagnetic interactions. In this picture, the electron is
paired with an anti-quark. Requiring exact gauge invariance for the
electromagnetic interaction clarifies the mechanism behind a recent proposal
for a lattice regularization of the standard model.


title: Phase Transitions

abstract:
  This is a set of notes on phase transitions and critical phenomena prepared
to accompany my lectures for the RHIC '97 summer school, held at Brookhaven
from July 6 to 16, 1997.


title:
Fermion theories on a 2d torus with Wilson action improved by Pauli --
  Villars regularization

abstract:
  Vectorial and anomaly free chiral U(1) fermion models on a 2d finite lattice
are considered. It is demonstrated both numerically and analytically that
introduction of Pauli -- Villars type regularization supresses the symmetry
breaking effects caused by the Wilson term.


title: Center Dominance, Center Vortices, and Confinement

abstract:
  We present a variety of numerical data supporting the Center Vortex theory of
confinement. A method is introduced for identifying the location of center
vortices, in thermalized gauge-field configurations generated by lattice Monte
Carlo. Fluctuations in the number of such vortices, linked to fundamental
representation Wilson loops, appear to be responsible for the asymptotic string
tension extracted from those loops.


title: The LHMC Algorithm for Free Field Theory: Reexamining Overrelaxation

abstract:
  We analyze the autocorrelations for the LHMC algorithm in the context of free
field theory. In this case this is just Adler's overrelaxation algorithm. We
consider the algorithm with even/odd, lexicographic, and random updates, and
show that its efficiency depends crucially on this ordering of sites when
optimized for a given class of operators. In particular, we show that, contrary
to previous expectations, it is possible to eliminate critical slowing down
(z[int]=0) for a class of interesting observables, including the magnetic
susceptibility: this can be done with lexicographic updates but is not possible
with even/odd (z[int]=1) or random (z[int]=2) updates. We are considering the
dynamical critical exponent z[int] for integrated autocorrelations rather than
for the exponential autocorrelation time; this is reasonable because it is the
integrated autocorrelation which determines the cost of a Monte Carlo
computation.


abstract:
  We describe the form factors for semileptonic B to rho l nu and radiative B
to K* gamma decays with just two parameters and the two form factors for
semileptonic B to pi l nu decays with three parameters. The parametrizations
are constrained by lattice results and are consistent with heavy quark
symmetry, kinematic constraints and light cone sum rule scaling relations.


title: Phase Transitions in SO(3) Lattice Gauge Theory

abstract:
  The phase diagram of SO(3) lattice gauge theory is investigated by Monte
Carlo techniques on both symmetric and asymmetric lattices with a view (i) to
understanding the relationship between the bulk transition and the
deconfinement transition, and (ii) to resolving the current ambiguity about the
nature of the high temperature phase. A number of tests, including an
introduction of a magnetic field and measurement of different correlation
functions in the phases with positive and negative values for the adjoint
Polyakov line, lead to the conclusion that the two phases correspond to the
same physical state. Studies on lattices of different sizes reveal only one
phase transition for this theory on all of them and it appears to have a
deconfining nature.


title: Branched polymers, complex spins and the freezing transition

abstract:
  We show that by coupling complex three-state systems to branched-polymer like
ensembles we can obtain models with gamma-string different from one half. It is
also possible to study the interpolation between dynamical and crystalline
graphs for these models; we find that only when geometry fluctuations are
completely forbidden is there a crystalline phase.


title: Disconnected Loop Noise Methods in Lattice QCD

abstract:
  A comparison of the noise variance between algorithms for calculating
disconnected loop signals in lattice QCD is carried out. The methods considered
are the Z(N) noise method and the Volume method. We find that the noise
variance is strongly influenced by the Dirac structure of the operator.


title: Multiple mass solvers

abstract:
  We present a general method to construct multiple mass solvers from standard
algorithms. As an example, the BiCGstab-M algorithm is derived.


title: Hybrid Quarkonia with High Statistics from NRQCD

abstract:
  We have studied the O(mv^6) effects in NRQCD on the spectrum of heavy
quarkonia and compare our results for different lattices (quenched and
dynamical). We also report on an investigation into hybrid states within the
framework of NRQCD. This suggests that the lowest lying hybrid is around the
B^* \bar B threshold and 3 standard deviations above the B \bar B.


title: Improved Upsilon Spectrum with Dynamical Wilson Fermions

abstract:
  We present results for the b \bar b spectrum obtained using an
O(M_bv^6)-correct non-relativistic lattice QCD action, where M_b denotes the
bare b-quark mass and v^2 is the mean squared quark velocity. Propagators are
evaluated on SESAM's three sets of dynamical gauge configurations generated
with two flavours of Wilson fermions at beta = 5.6. These results, the first of
their kind obtained with dynamical Wilson fermions, are compared to a quenched
analysis at equivalent lattice spacing, beta = 6.0. Using our three sea-quark
values we perform the ``chiral'' extrapolation to m_eff = m_s/3, where m_s
denotes the strange quark mass. The light quark mass dependence is found to be
small in relation to the statistical errors. Comparing the full QCD result to
our quenched simulation we find better agreement of our dynamical data with
experimental results in the spin-independent sector but observe no unquenching
effects in hyperfine-splittings. To pin down the systematic errors we have also
compared quenched results in different ``tadpole'' schemes as well as using a
lower order action. We find that spin-splittings with an O(M_bv^4) action are
O(10%) higher compared to O(M_bv^6) results. Relative to the results obtained
with the plaquette method the Landau gauge mean link tadpole scheme raises the
spin splittings by about the same margin so that our two improvements are
opposite in effect.


title: Vertex Models on Feynman Diagrams

abstract:
  The statistical mechanics of spin models, such as the Ising or Potts models,
on generic random graphs can be formulated economically by considering the N
--> 1 limit of Hermitian matrix models. In this paper we consider the N --> 1
limit in complex matrix models, which describes vertex models of different
sorts living on random graphs. From the graph theoretic perspective one is
using matrix model and field theory inspired methods to count various classes
of directed graphs.
  We also make some remarks on vertex models on planar random graphs (the N -->
infinity limit) where the resulting matrix models are not generally soluble
using currently known methods. Nonetheless, some particular cases may be mapped
onto known models and hence solved.


title:
A High Statistics Lattice Calculation of Quark Masses with a
  Non-Perturbative Renormalization Procedure

abstract:
  We present results of a high statistics study (O(2000) configurations) of the
quark masses in the MS-bar scheme from Lattice QCD in the quenched
approximation at beta=6.0, beta=6.2 and beta=6.4 using both the Wilson and the
tree-level improved SW-Clover fermion action. We extract quark masses from the
meson spectroscopy and from the axial Ward Identity using non-perturbative
values of the renormalization constants. We compare the results obtained with
the two methods and we study the O(a) dependence of the quark masses for both
actions. Our best results are m_s^(MS-bar)(2 GeV)=(123 +- 4 +- 15) MeV and
m_c^(MS-bar)(2 GeV)=(1525 +- 40 +- 100) MeV.


title: A disorder parameter for dual superconductivity in gauge theories

abstract:
  Dual superconductivity in the confining phase of gauge theories is discussed
in terms of a disorder parameter which vanishes in normal phase and is
different from zero in the superconducting phase.


title: Block Spin Effective Action for Polyakov Loops in 4D SU(2) LGT

abstract:
  Using a variant of the IMCRG method of Gupta and Cordery, we explicitly
compute majority rule block spin effective actions for the signs of the
Polyakov loops in 4D SU(2) finite temperature lattice gauge theories. To the
best of our knowledge, this is the first attempt to compute numerically
effective actions for the Polyakov loop degrees of freedom in 4D SU(2). The
most important observations are: 1. The renormalization group flow at the
deconfinement transition can be nicely matched with the flow of the 3D Ising
model, thus confirming the Svetitsky-Yaffe conjecture. 2. The IMCRG simulations
of the FT SU(2) model have strongly reduced critical slowing down.


title: Singular Structure in 4D Simplicial Gravity

abstract:
  We show that the phase transition previously observed in dynamical
triangulation models of quantum gravity can be understood as being due to the
creation of a singular link. The transition between singular and non-singular
geometries as the gravitational coupling is varied appears to be first order.


title:
New Estimates On Various Critical/Universal Quantities of the 3D Ising
  Model

abstract:
  We present estimates for the 3D Ising model on the cubic lattice, both
regarding interface and bulk properties. We have results for the interface
tension, in particular the amplitude sigma0 in the critical law sigma =
sigma0*t**mu, and for the universal combination R_ = sigma*xi**2. Concerning
the bulk properties, we estimate the specific heat universal amplitude ratio
A+/A_, together with the exponent alpha, the nonsingular background of energy
and specific heat at criticality, together with the exponent nu. There are also
results for the universal combination fs*xi**3, where fs is the singular part
of the free energy.


title:
Magnetic monopole clusters, and monopole dominance after smoothing in
  the maximally Abelian gauge of SU(2)

abstract:
  In the maximally Abelian gauge of SU(2), the clusters of monopole current are
found to divide into two distinct classes. The largest cluster permeates the
lattice, has a density that scales and produces the string tension. The
remaining clusters possess an approximate 1/l^3 number density distribution (l
is the cluster length), their radii vary as \sqrt l and their total current
density does not scale. Their contribution to the string tension is compatible
with being exactly zero. Their number density can be thought of as arising from
an underlying scale invariant distribution. This suggests that they are not
related to instantons. We also observe that when we locally smoothen the SU(2)
fields by cooling, the string tension due to monopoles becomes much smaller
than the SU(2) string tension. This dramatic loss of Abelian/monopole dominance
occurs even after just one cooling step.


title: NRQCD Results on Form Factors

abstract:
  We report results on $f_B$ and semi-leptonic $B$ decay form factors using
NRQCD. We investigate $1/M$ scaling behavior of decay amplitudes. For $f_B$
Effect of higher order relativistic correction terms are also studied.


title:
Direct determination of the gauge coupling derivatives for the energy
  density in lattice QCD

abstract:
  By matching Wilson loop ratios on anisotropic lattices we measure the
coefficients $\cs$ and $\ct$, which are required for the calculation of the
energy density. The results are compared to that of an indirect method of
determination. We find similar behaviour, the differences are attributed to
different discretization errors.


title: Fixed point actions in SU(3) gauge theory: surface tension and topology

abstract:
  This work is organized in two independent parts. In the first part are
presented some results concerning the surface tension in SU(3) obtained with a
parametrized fixed point action. In the second part, a new, approximately
scale-invariant, parametrized fixed point action is proposed which is suitable
to study the topology in SU(3).


title: The fixed point action of the Schwinger model

abstract:
  We compute the fixed point action for the Schwinger model through an
expansion in the gauge field. The calculation allows a check of the locality of
the action. We test its perfection by computing the 1-loop mass gap at finite
spatial volume.


title: The Overlap Formalism and Topological Susceptibility on the Lattice

abstract:
  Recent lattice measurements of the topological susceptibility of SU(2) gauge
theory using improved cooling and inverse-blocking are in disagreement. We use
the overlap method, which probes the fermionic sector of the theory directly,
to help resolve this discrepancy.


title: Infrared Behavior of the Gluon Propagator in Lattice Landau Gauge

abstract:
  We evaluate numerically the four-momentum-space gluon propagator in lattice
Landau gauge, for pure SU(2) lattice gauge theory with periodic boundary
conditions. Simulations are done in the strong-coupling regime, namely at
$\beta = 0, 0.8, 1.2 and 1.6$, and for lattice sizes up to $30^4, 16^4, 20^4
and 24^4$ respectively. In the limit of large lattice volume, we observe in all
cases a gluon propagator decreasing as the momentum goes to zero. This
counter-intuitive result has a straightforward interpretation as resulting from
the proximity of the so-called first Gribov horizon in infrared directions.


title: Improved Quenched QCD on Large Lattices - First Results

abstract:
  Continuing our investigations of quenched QCD with improved fermions we have
started simulations for lattice size 32^3 x 64 at beta=6.2. We present first
results for light hadron masses at kappa=0.13520, 0.13540, and 0.13555.
Moreover we compare our initial experiences on the T3E with those for
APE/Quadrics systems.


title: Flux tubes and their interaction in U(1) lattice gauge theory

abstract:
  We investigate singly and doubly charged flux tubes in U(1) lattice gauge
theory. By simulating the dually transformed path integral we are able to
consider large flux tube lengths, low temperatures, and multiply charged
systems without loss of numerical precision. We simulate flux tubes between
static sources as well as periodically closed flux tubes, calculating flux tube
profiles, the total field energy and the free energy. Our main results are that
the string tension in both three and four dimensions scales proportionally to
the charge -- which is in contrast to previous lattice results -- and that in
four-dimensional U(1) there is an attractive interaction between flux tubes for
beta approaching the phase transition.


title: A fixed-point action for the lattice Schwinger model

abstract:
  We determine non-perturbatively a fixed-point (FP) action for fermions in the
two-dimensional U(1) gauge (Schwinger) model. Our parameterization for the
fermionic action has terms within a $7\times 7$ square on the lattice, using
compact link variables. With the Wilson fermion action as starting point we
determine the FP-action by iterating a block spin transformation (BST) with a
blocking factor of 2 in the background of non-compact gauge field
configurations sampled according to the (perfect) Gaussian measure. We simulate
the model at various values of $\beta$ and find excellent improvement for the
studied observables.


title: The endpoint of the electroweak phase transition

abstract:
  The 3d SU(2)-Higgs model is used to find the critical Higgs mass above which
the first order phase transition ends. One method is focused on the
disappearance of the two-state signal of the scalar condensate (vanishing of
the latent heat). Another method is based on the analysis of Lee-Yang zeroes of
the partition function which allows to characterise the change from first order
transition into an analytical crossover.


title: Hot electroweak matter near to the endpoint of the phase transition

abstract:
  The electroweak phase transition is investigated near to its endpoint in the
framework of an effective three-dimensional model. We measure the very weak
interface tension with the tunneling correlation length method. First results
for the mass spectrum and the corresponding wave functions in the symmetric
phase are presented.


title: Dual variables for the SU(2) lattice gauge theory at finite temperature

abstract:
  We study the three-dimensional SU(2) lattice gauge theory at finite
temperature using an observable which is dual to the Wilson line. This
observable displays a behaviour which is the reverse of that seen for the
Wilson line. It is non-zero in the confined phase and becomes zero in the
deconfined phase. At large distances, it's correlation function falls off
exponentially in the deconfined phase and remains non-zero in the confined
phase. The dual variable is non-local and has a string attached to it which
creates a Z(2) interface in the system. It's correlation function measures the
string tension between oppositely oriented Z(2) domains. The construction of
this variable can also be made in the four-dimensional theory where it measures
the surface tension between oppositely oriented Z(2) domains.


title: The non-perturbative O(a)-improved action for dynamical Wilson fermions

abstract:
  We compute the improvement coefficient $c_{sw}$ that multiplies the
Sheikholeslami-Wohlert term as a function of the bare gauge coupling for two
flavour QCD. We discuss several aspects concerning simulations with improved
dynamical Wilson fermions.


title: Monopole percolation in scalar QED

abstract:
  Monopole Percolation was first introduced in the study of the non-compact
lattice QED in both, the pure case and coupled to Higgs fields. Monopole
percolation has been also observed coupled to the monopole condensation in the
study of the pure gauge compact QED. We present here the results coming from
the analysis of the role of the monopole percolation in the coupled gauge-higgs
compact QED.


title: High-T QCD and dimensional reduction: measuring the Debye mass

abstract:
  We study the high-temperature phase of SU(2) and SU(3) QCD using lattice
simulations of an effective 3-dimensional SU(N) + adjoint Higgs -theory,
obtained through dimensional reduction. We investigate the phase diagram of the
3D theory, and find that the high-T QCD phase corresponds to the metastable
symmetric phase of the 3D theory. We measure the Debye screening mass m_D with
gauge invariant operators; in particular we determine the O(g^2) and O(g^3)
corrections to m_D. The corrections are seen to be large, modifying the
standard power-counting hierarchy in high temperature QCD.


title: The Quantum Spacetime of c>0 2d Gravity

abstract:
  We review recent developments in the understanding of the fractal properties
of quantum spacetime of 2d gravity coupled to c>0 conformal matter. In
particular we discuss bounds put by numerical simulations using dynamical
triangulations on the value of the Hausdorff dimension d_H obtained from
scaling properties of two point functions defined in terms of geodesic
distance. Further insight to the fractal structure of spacetime is obtained
from the study of the loop length distribution function which reveals that the
0<c<= 1 system has similar geometric properties with pure gravity, whereas the
branched polymer structure becomes clear for c >= 5.


title:
Remarks on the realization of the Atiyah-Singer index theorem in lattice
  gauge theory

abstract:
  We discuss the interplay between topologically non-trivial gauge field
configurations and the spectrum of the Wilson-Dirac operator in lattice gauge
theory. Our analysis is based on analytic arguments and numerical results from
a lattice simulation of QED_2.


title: The twisted Wilson fermion for the Standard Model on a lattice

abstract:
  We present a preliminary study of a chiral-gauge-invariant Wilson term for
the Standard Model on a lattice. In the strong coupling limit for doublers,
this Wilson term shows that the doublers of leptons (quarks) are anti-baryons
(anti-leptoquarks), and they are decoupled by getting gauge invariant masses.
We discuss that the possibility of achieving the low-energy Standard Model
could be realized by the ``three-fermion-cuts'' at the weak coupling limit for
normal modes, where baryons and leptoquarks dissolve into their constituents.


title: First Lattice Study of Semileptonic Decays of Lambda_b and Xi_b Baryons

abstract:
  We present the results of the first lattice study of semileptonic decays of
baryons containing a b-quark. Predictions for the decay distributions are given
and the Isgur-Wise functions for heavy baryons are computed, for values of the
velocity transfer up to about omega=1.2. The computations are performed on a
24^3 x 48 lattice at beta=6.2 using the Sheikholeslami-Wohlert action in the
quenched approximation.


title: B spectroscopy using all-to-all propagators

abstract:
  We measure the ground and excited states for B mesons in the static limit
using maximally variance reduced estimators for light quark propagators.
Because of the large number of propagators we are able to measure accurately
also orbitally excited P, D and F states. We also present some results for
Lambda_b.


title: Chiral symmetry in the 2-flavour lattice Schwinger model

abstract:
  We study the 2-flavour lattice Schwinger model: QED in D=2 with two fermion
species of identical mass. In the simulation we are using Wilson fermions where
chiral symmetry is explicitly broken. Since there is no known simple order
parameter it is non-trivial to identify the critical line of the chiral phase
transition. We therefore need to find observables which allow an identification
of a possible restoration of chiral symmetry. We utilize the PCAC-relations in
order to identify the critical coupling, where chiral symmetry is restored.


title: Field strength correlators in QCD with dynamical fermions

abstract:
  We determine, by numerical simulations on a lattice, the gauge-invariant
two-point correlation functions of the gauge field strengths in the QCD vacuum
with four flavours of dynamical staggered fermions.


title: Center Vortices and the Asymptotic String Tension

abstract:
  We present a method for locating center vortices (``fluxons'') in thermalized
lattice gauge field configurations. We find evidence, in lattice Monte Carlo
simulations, that the asymptotic string tension of fundamental-representation
Wilson loops is due to fluctuations in the number of center vortices linking
those loops.


title: Experiences with the Polynomial Hybrid Monte Carlo Algorithm

abstract:
  We discuss a simulation algorithm for dynamical fermions, which combines the
multiboson technique with the Hybrid Monte Carlo algorithm. The algorithm turns
out to give a substantial gain over standard methods in practical simulations
and to be suitable for dealing with fermion zero modes in a clean and
controllable way.


title: Chiral symmetry breaking in the 3-d Thirring model for small $N_f$

abstract:
  We study the dynamical breaking of chiral symmetry in the 3-d Thirring model
for a small number of fermion species. The critical point is identified by
fitting lattice data to an equation of state. The spectrum of the theory is
studied to confirm the phase structure of the model.


title:
Improving the staggered quark action to reduce flavour symmetry
  violations

abstract:
  We investigate a class of actions for lattice QCD with staggered quarks aimed
at reducing the flavour symmetry violations associated with using staggered
fermions. These actions replace the gauge field link fields in the quark action
with covariantly smeared fields. As such they are an extension of actions
considered by the MILC collaboration. We show that such actions systematically
reduce flavour symmetry violations in the weak coupling limit. Using the mass
splitting between Goldstone and non-Goldstone pions as a measure of flavour
symmetry violations we find that these actions have considerably less flavour
symmetry violations than the standard staggered action, and represent an
improvement on what can be achieved with the MILC action, on quenched
configurations with $\beta=5.7$.


title: $O(a)$ Improvement of Nucleon Matrix Elements

abstract:
  We report on preliminary results of a high statistics quenched lattice QCD
calculation of nucleon matrix elements within the Symanzik improvement
programme. Using the recently determined renormalisation constants from the
Alpha Collaboration we present a fully non-pertubative calculation of the
forward nucleon axial matrix element with $O(a)$ lattice artifacts completely
removed. Runs are made at $\beta=6.0$ and $\beta=6.2$, in an attempt to check
scaling and $O(a^2)$ effects. We shall also briefly describe results for $<x>$,
the matrix element of a higher derivative operator.


title: Lattice Chiral Schwinger Model in the Continuum Formulation

abstract:
  We pursue further an approach to lattice chiral fermions in which the
fermions are treated in the continuum. To render the effective action gauge
invariant, counterterms have to be introduced. We determine the counterterms
for smooth gauge fields, both analytically and numerically. The final result is
that the imaginary part of the effective action can be computed analytically
from the lattice gauge field, while the real part is given by one half of the
action of the corresponding vector model.


title: Abelian monopoles in lattice gluodynamics as physical objects

abstract:
  By numerical calculations we show that the abelian monopole currents are
locally correlated with the density of SU(2) lattice action. This fact is
established for the maximal abelian projection. Thus, in the maximal abelian
projection the monopoles are physical objects, they carry SU(2) action.
Calculations on the asymmetric lattice show that the correlation between
monopole currents and the density of SU(2) lattice action also exists in the
deconfinement phase of gluodynamics.


title: Electric and magnetic currents in SU(2) lattice gauge theory

abstract:
  The correlations of the topological charge (Q), the electric (Je) and the
magnetic (Jm) currents in the SU(2) lattice gauge theory in the Maximal Abelian
projection are investigated. A nonzero value of the correlator <Q Je Jm> is
obtained for a wide range of values of the bare charge, as well as under the
cooling.


title: The fixed point action for the Schwinger model: a perturbative approach

abstract:
  We compute the fixed point action of a properly defined renormalization group
transformation for the Schwinger model through an expansion in the gauge field.
It is local, with couplings exponentially suppressed with the distance. We
check its perfection by computing the 1-loop mass gap at finite spatial volume,
finding only exponentially vanishing cut off effects, in contrast with the
standard action, which is affected by large power-like cut off effects. We
point out that the 1-loop mass gap calculation provides a check of the
classical perfection of the fixed point action, and not of the 1-loop
perfection, as could be naively expected.


title: Log Triviality in the Nambu -- Jona-Lasinio Model

abstract:
  Results are presented from a Monte Carlo simulation of the Nambu --
Jona-Lasinio model with SU(2)xSU(2) chiral symmetry and N_f=2 flavors of
fermion. We show that fits to the equation of state are sensitive to the shape
and extent of the assumed scaling region; the best fits favour a triviality
scenario predicted by the large-N_f approximation, in which the scalar degrees
of freedom are fermion -- anti-fermion composites with wavefunction
renormalisation constant vanishing logarithmically in the continuum limit.


title: Z(2) vortices and the string tension in SU(2) gauge theory

abstract:
  We exhibit the appropriate variables allowing the plus-minus (Z(2))
`reduction' of the Wilson loop operator which provides a direct measure of the
thin, thick and `mixed' Z(2) topological, gauge-invariant vortices in SU(2)
LGT. Simulations with the Wilson action, as well as a perfect action smoothing
procedure, show the string tension to be reproduced from the contributions of
these excitations.


title: Heavy-Light Meson Decay Constants on the Lattice

abstract:
  We present a high statistics study of the D- and B-meson decay constants. The
results were obtained by using the Clover and Wilson lattice actions at
$\beta=6.0$ and 6.2.


title: Non-Perturbative Renormalisation and Kaon Physics

abstract:
  A general review is presented on the problem of non perturbative computation
of the $K\to\pi\pi$ transition amplitude.


title: Finite Temperature Meson Masses with Improved Quenched Wilson Fermions

abstract:
  We present recent results for meson screening masses with quenched Wilson
fermions above and below the confinement- deconfinement phase transition. The
action used in the simulation is the Sheikholeslami Wohlert action. The quark
masses are chosen to be in a range going from light quarks up to the mass of
the charm quark. These results are compared with zero temperature Wilson and
high temperature staggered data.


title: QCD Sum Rules on the Lattice

abstract:
  We study the work of Leinweber by applying the Continuum Model of QCD Sum
Rules (QCDSR) to the analysis of (quenched) lattice correlation functions. We
expand upon his work in several areas and find that, while the QCDSR Continuum
Model very adequately fits lattice data, it does so only for non-physical
values of its parameters. The non-relativistic model is found to predict
essentially the same form for the correlation functions as the QCDSR Continuum
Model but without the latter's restrictions. By fitting lattice data to a
general form which includes the non-relativistic quark model as a special case,
we confirm it as the model of choice.


title:
Magnetic Monopoles as Agents of Chiral Symmetry Breaking in U(1) Lattice
  Gauge Theory

abstract:
  We present results suggesting that magnetic monopoles can account for chiral
symmetry breaking in abelian gauge theory. Full U(1) configurations from a
lattice simulation are factorized into magnetic monopole and photon
contributions. The expectation <psibarpsi> is computed using the monopole
configurations and compared to results for the full U(1) configurations. It is
shown that excellent agreement between the two values of <psibarpsi> is
obtained if the effect of photons, which "dress" the composite operator
psibarpsi, is included. This can be estimated independently by measurements of
the physical fermion mass in the photon background.


title: Comparing improved actions for SU(2)

abstract:
  In order to help the user in choosing the right action a performance
comparison is done for seven improved actions. Six of them are Symanzik
improved, one at tree-level and two at one-loop, all with or without tadpole
improvement. The seventh is an approximate fixed point action. Observables are
static on- and off-axis two-body potentials and four-body binding energies,
whose precision is compared when the same amount of computer time is used by
the programs.


title: Perturbative Renormalization of Improved Lattice Operators

abstract:
  We derive bases of improved operators for all bilinear quark currents up to
spin two (including the operators measuring the first moment of DIS Structure
Functions), and compute their one-loop renormalization constants for arbitrary
coefficients of the improvement terms. We have thus control over O(a)
corrections, and for a suitable choice of improvement coefficients we are only
left with errors of O(a^2).


title: Extension of a new method for locating critical temperatures

abstract:
  We investigate recently proposed method for locating critical temperatures
and introduce some modifications which allow to formulate exact criterion for
any self-dual model. We apply the modified method for the Ashkin-Teller model
and show that the exact result for a critical temperature is reproduced. We
test also a two-layer Ising model for the presence of eventual self-duality.


title: The Mass Spectrum of a Static Adjoint Particle

abstract:
  The bound states of fermions in the adjoint representation are of interest in
supersymmetric models. We investigate the energy spectrum of the simplest --
the gluino-gluon bound states -- on several lattices in the quenched
approximation. We use a static approximation for the gluino propagator. We find
continuum limits of the splitting between the few lowest states, with the
energy difference between the two lowest states of $354 \pm 9$ MeV.


title: Scaling Tests of Some Lattice Fermion Actions

abstract:
  I describe studies of quenched spectroscopy, using crude approximations to
fixed point actions for fermions interacting with SU(3) gauge fields. These
actions have a hypercubic kinetic term and a complicated lattice anomalous
magnetic moment term. They show improved scaling compared to the conventional
Wilson action.