title: B Meson Decay Constants From NRQCD

abstract:
  We present quenched results for B meson decay constants using NRQCD b quarks
and O(a) tadpole improved clover light quarks. For the first time, one-loop
matching factors between lattice and continuum currents are incorporated
through O(\alpha/M) taking operator mixing fully into account. This includes an
important O(\alpha a) discretization correction to the heavy-light axial vector
current. We find f_B = 0.147(11)(^{+8}_{-12})(9)(6) MeV and f_{B_s}/f_B =
1.20(4)(^{+4}_{-0}).
  PACS numbers: 12.38.Gc, 12.39.Hg, 13.20.He, 14.40.Nd


title:
SU(3) Flavor Breaking in Hadronic Matrix Elements for $B - \bar B$
  Oscillations

abstract:
  Results in the quenched approximation for SU(3) breaking ratios of the
heavy-light decay constants and the $\Delta F=2$ mixing matrix elements are
reported. Using lattice simulations at $6/g^2=5.7$, 5.85, 6.0, and 6.3, we
directly compute the mixing matrix element $M_{hl}=< \bar P_{hl}|\bar h
\gamma_\mu (1-\gamma_5)l \bar h \gamma_\mu(1-\gamma_5)l|P_{hl}>$. Extrapolating
to the physical B meson states, $B^0$ and $B_s^0$, we obtain $M_{bs}/M_{bd}
=1.76(10)^{+57}_{-42}$. in the continuum limit. The systematic error includes
the errors within the quenched approximation but not the errors of quenching.
We also obtain the ratio of decay constants,
$f_{bs}/f_{bd}=1.17(2)^{+12}_{-6}$. For the B parameters we find $B_{bs}(2
GeV)=B_{bd}(2 GeV)=1.02(13)$; we cannot resolve the SU(3) breaking effects in
this case.


title:
Action and topological density carried by Abelian monopoles in finite
  temperature pure SU(2) gauge theory: an analysis using RG smoothing

abstract:
  We test a new parametrization of a suitably truncated classically perfect
action for SU(2) pure gauge theory with respect to self-consistency and locate
the deconfinement transition on a 12^3X4 lattice. Using the technique of
smoothing (blocking followed by inverse blocking) we demonstrate clustering of
action and topological charge density. Concentrating on the Abelian monopoles
found in smoothed configurations after Abelian projection from the maximally
Abelian gauge, we present evidence for their role as carriers of non-Abelian
action and topological charge.


title: Accurate Checks of Universality for Dyson's Hierarchical Model

abstract:
  Using recently developed methods, we perform high-accuracy calculations of
the susceptibility near beta_c for the D=3 version of Dyson's hierarchical
model. Using linear fits, we estimate the leading gamma and subleading Delta
exponents. Independent estimates are obtained by calculating the first two
eigenvalues of the linearized renormalization group transformation. We found
gamma = 1.29914073 (with an estimated error of 10^{-8}) and, Delta=0.4259469
(with an estimated error of 10^{-7}) independently of the choice of local
integration measure (Ising or Landau-Ginzburg). After a suitable rescaling, the
approximate fixed points for a large class of local measure coincide accurately
with a fixed point constructed by Koch and Wittwer.


title:
Use of even Grassmann variables to construct effective actions for
  mesons

abstract:
  A quadratic action in even Grassmann variables with the quantum numbers of
the pions has been studied. It includes the $\sigma$-field in order to be
invariant under SU(2)_L times SU(2)_R transformations over the quarks. This
action exhibits the Goldstone phenomenon reducing its symmetry to the O(3)
isospin invariance. The model has been investigated in the
Stratonovitch-Hubbard representation, in which form it is reminiscent of the
Gell-Mann-Levy model. By the saddle point method a renormalizable expansion in
inverse powers of the index of nilpotency of the mesonic fields (which is 24),
is generated. The way it might be used in a new perturbative approach to QCD is
outlined.


title:
Center dominance, Casimir scaling, and confinement in lattice gauge
  theory

abstract:
  We present numerical evidence that supports the theory of quark confinement
based on center vortex condensation. We introduce a special gauge ("maximal
center gauge") and center projection, suitable for identification of center
vortices. Main focus is then put on the connection of vortices in center
projection to "confiners" in full, unprojected gauge-field configurations.
Topics briefly discussed include: the relation between vortices and monopoles,
first results for SU(3), and the problem of Casimir scaling.


title:
First Order Phase Transition in Finite Density QCD using the modulus of
  the Dirac Determinant

abstract:
  We report results of simulations of strong coupling, finite density QCD
obtained within a MFA inspired approach where the fermion determinant in the
integration measure is replaced by its absolute value. Contrary to the standard
wisdom, we show that within this approach a clear signal of a phase transition
appears with a critical chemical potential in extremely good agreement with the
results obtained with the Glasgow algorithm. The modulus of the fermion
determinant seems therefore to preserve some of the relevant physical
properties of the system. We also analyze the dependence of our results on the
quark mass, including both the chiral and large mass limit, and the theory in
the quenched approximation.


title: Probing the QCD Vacuum with Static Sources in Maximal Abelian Projection

abstract:
  Various field strength correlators are investigated in the maximal Abelian
projection of pure SU(2) lattice gauge theory. High precision measurements of
the colour fields, monopole currents, their curls and divergences allow for
detailed checks of the dual superconductor scenario. On this basis, we perform
a Ginzburg-Landau type analysis of the flux tube profile from which we derive
the size of the penetration length, LAMBDA = 0.16(2) fm, and coherence length
of the monopole condensate wave function, XI = 0.27(3) fm. The ratio of these
numbers is KAPPA = LAMBDA/XI = 0.59(13) which is below the value 1/SQRT(2)
where type II superconductivity sets in.


title: Renormalization group coupling flow of SU(3) gauge theory

abstract:
  We present our new results on the renormalization group coupling flow
obtained i n 3 dimensional coupling space
$(\beta_{11},\beta_{12},\beta_{twist})$. The value of $\beta_{twist}$ turns out
to be small and the coupling flow projected on $(\beta_{11},\beta_{12})$ plane
is very similar with the previous result obtained in the 2 dimensional coupling
space.


title: Lattice QCD without tuning, mixing and current renormalization

abstract:
  The classically perfect action of QCD requires no tuning to get the pion
massless in the broken phase: the critical bare mass $m_q^c$ is zero. Neither
the vector nor the flavour non-singlet axial vector currents need
renormalization. Further, there is no mixing between four-fermion operators in
different chiral representations. The order parameter of chiral symmetry
requires, however, a subtraction which is given here explicitly. These results
are based on the fact that the fixed point action satisfies the Ginsparg-Wilson
remnant chiral symmetry condition. On chiral symmetry related questions any
other local solution of this condition will produce similar results.


title: Monopole condensation and colour confinement

abstract:
  The evidence is reviewed for the mechanism of colour confinement in QCD by
dual superconductivity of the ground state, i.e. by condensation of monopoles.


title:
Properties of the Fixed Point Lattice Dirac Operator in the Schwinger
  Model

abstract:
  We present a numerical study of the properties of the Fixed Point lattice
Dirac operator in the Schwinger model. We verify the theoretical bounds on the
spectrum, the existence of exact zero modes with definite chirality, and the
Index Theorem. We show by explicit computation that it is possible to find an
accurate approximation to the Fixed Point Dirac operator containing only very
local couplings.


title: Common Structures in Simplicial Quantum Gravity

abstract:
  The statistical properties of dynamically triangulated manifolds (DT mfds) in
terms of the geodesic distance have been studied numerically. The string
susceptibility exponents for the boundary surfaces in three-dimensional DT mfds
were measured numerically. For spherical boundary surfaces, we obtained a
result consistent with the case of a two-dimensional spherical DT surface
described by the matrix model. This gives a correct method to reconstruct
two-dimensional random surfaces from three-dimensional DT mfds. Furthermore, a
scaling property of the volume distribution of minimum neck baby universes was
investigated numerically in the case of three and four dimensions, and we
obtain a common scaling structure near to the critical points belonging to the
strong coupling phase in both dimensions. We have evidence for the existence of
a common fractal structure in three- and four-dimensional simplicial quantum
gravity.


title: Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation

abstract:
  It is shown that the Ginsparg-Wilson relation implies an exact symmetry of
the fermion action, which may be regarded as a lattice form of an infinitesimal
chiral rotation. Using this result it is straightforward to construct lattice
Yukawa models with unbroken flavour and chiral symmetries and no doubling of
the fermion spectrum. A contradiction with the Nielsen-Ninomiya theorem is
avoided, because the chiral symmetry is realized in a different way than has
been assumed when proving the theorem.


title: Tests of Hypercubic Fermion Actions

abstract:
  I have performed scaling tests using quenched spectroscopy of a family of
fermion actions which have a hypercubic kinetic term, gauge connections built
of smeared links, and an anomalous magnetic moment term. These actions show
improved rotational invariance compared to the standard Wilson action and to
the tadpole-improved clover action. Hyperfine splittings are improved compared
to the standard Wilson action (at the level of a factor of three in the lattice
spacing), and are about the same as for the tadpole-improved clover action.


title:
Lattice perturbation theory in the overlap formulation for the Yukawa
  and gauge interactions

abstract:
  Lattice perturbation theory is discussed in the overlap formulation for the
Yukawa and gauge interactions. One and two point functions are studied for
fermion, scalar and gauge fields, taking the Standard Model as an example. The
formulae for the self-energies are given from which their divergent and finite
parts can be computed at the one loop level.


title: Perfect and Quasi-Perfect Lattice Actions

abstract:
  Perfect lattice actions are exiting with several respects: they provide new
insight into conceptual questions of the lattice regularization, and
quasi-perfect actions could enable a great leap forward in the non-perturbative
solution of QCD. We try to transmit a flavor of them, also beyond the lattice
community.


title:
Maximal variance reduction for stochastic propagators with applications
  to the static quark spectrum

abstract:
  We study a new method -- maximal variance reduction -- for reducing the
variance of stochastic estimators for quark propagators. We find that while
this method is comparable to usual iterative inversion for light-light mesons,
a considerable improvement is achieved for systems containing at least one
infinitely heavy quark. Such systems are needed for heavy quark effective
theory. As an illustration of the effectiveness of the method we present
results for the masses of the ground state and excited states of $\bar{Q}q$
mesons and $\bar{Q}qq$ baryons. We compare these results with the experimental
spectra involving $b$ quarks.


title: Spectral flow, condensate and topology in lattice QCD

abstract:
  We study the spectral flow of the Wilson-Dirac operator H(m) with and without
an additional Sheikholeslami-Wohlert (SW) term on a variety of SU(3) lattice
gauge field ensembles in the range $0\le m \le 2$. We have used ensembles
generated from the Wilson gauge action, an improved gauge action, and several
two-flavor dynamical quark ensembles. Two regions in $m$ provide a generic
characterization of the spectrum. In region I defined by $m\le m_1$, the
spectrum has a gap. In region II defined by $m_1\le m \le 2$, the gap is
closed. The level crossings in H(m) that occur in region II correspond to
localized eigenmodes and the localization size decreases monotonically with the
crossing point down to a size of about one lattice spacing. These small modes
are unphysical, and we find the topological susceptibility is relatively stable
in the part of region II where the small modes cross. We argue that the lack of
a gap in region II is expected to persist in the infinite volume limit at any
gauge coupling. The presence of a gap is important for the implementation of
domain wall fermions.


title: Topological Properties of the QCD Vacuum at T=0 and T ~ T_c

abstract:
  We study on the lattice the topology of SU(2) and SU(3) Yang-Mills theories
at zero temperature and of QCD at temperatures around the phase transition. To
smooth out dislocations and the UV noise we cool the configurations with an
action which has scale invariant instanton solutions for instanton size above
about 2.3 lattice spacings. The corresponding "improved" topological charge
stabilizes at an integer value after few cooling sweeps. At zero temperature
the susceptibility calculated from this charge (about (195MeV)^4 for SU(2) and
(185 MeV)^4 for SU(3)) agrees very well with the phenomenological expectation.
At the minimal amount of cooling necessary to resolve the structure in terms of
instantons and anti-instantons we observe a dense ensemble where the total
number of peaks is by a factor 5-10 larger than the net charge. The average
size observed for these peaks at zero temperature is about 0.4-0.45 fm for
SU(2) and 0.5-0.6 fm for SU(3). The size distribution changes very little with
further cooling, although in this process up to 90% of the peaks disappear by
pair annihilation. For QCD we observe below T_c a reduction of the topological
susceptibility as an effect of the dynamical fermions. Nevertheless also here
the instantons form a dense ensemble with general characteristics similar to
those of the quenched theory. A further drop in the susceptibility above T_c is
also in rough agreement with what has been observed for pure SU(3). We see no
clear signal for dominant formation of instanton - anti-instanton molecules.


title: Ginsparg-Wilson relation and the overlap formula

abstract:
  The fermionic determinant of a lattice Dirac operator that obeys the
Ginsparg-Wilson relation factorizes into two factors that are complex conjugate
of each other. Each factor is naturally associated with a single chiral fermion
and can be realized as a overlap of two many body vacua.


title:
Truncation Effects in Monte Carlo Renormalization Group Improved Lattice
  Actions

abstract:
  We study truncation effects in the SU(3) gauge actions obtained by the Monte
Carlo renormalization group method. By measuring the heavy quark potential we
find that the truncation effects in the actions coarsen the lattice by 40-50 %
from the original blocked lattice. On the other hand, we find that rotational
symmetry of the heavy quark potentials is well recovered on such coarse
lattices, which may indicate that rotational symmetry breaking terms are easily
cancelled out by adding a short distance operator. We also discuss the
possibility of reducing truncation effects.


title:
The Monotony Criterion for A Finite Size Scaling Analysis of Phase
  Transitions

abstract:
  We propose a new criterion to analyse the order of phase transitions within a
finite size scaling analysis. It refers to response functions like order
parameter susceptibilities and the specific heat and states different monotony
behaviour in volume for first and second order transitions close to the
transition point. The criterion applies to analytical and numerical studies of
phase diagrams including tricritical behaviour.


title:
Multicanonical simulation of 3D dynamical triangulation model and a new
  phase structure

abstract:
  We apply the multicanonical technique to the three dimensional dynamical
triangulation model, which is known to exhibit a first order phase transition
with the Einstein-Hilbert action. We first clarify the first order nature of
the phase transition with the Einstein-Hilbert action in several ways including
a high precision finite size scaling analysis. We then add a new local term to
the action and confirm the conjecture made through the MCRG technique that the
line of the first order phase transition extends to the expanded phase diagram,
ending at a point. Fractal dimension at the end point is measured to be around
three up to the present size.


title: A Monte Carlo study of Inverse Symmetry Breaking

abstract:
  We make a Monte Carlo study of the coupled two-scalar
$\lambda\phi^2_1\phi^2_2$ model in four dimensions at finite temperature. We
find no trace of Inverse Symmetry Breaking for values of the renormalized
parameters for which perturbation theory predicts this phenomenon.


title: Hopping Parameter Series Construction for Models with Nontrivial Vacuum

abstract:
  Hopping parameter expansions are convergent power series. Under general
conditions they allow for the quantitative investigation of phase transition
and critical behaviour. The critical information is encoded in the high order
coefficients. Recently, 20th order computations have become feasible and used
for a large class of lattice field models both in finite and infinite volume.
They have been applied to quantum spin models and field theories at finite
temperature. The models considered are subject to a global ${\bf Z}_2$ symmetry
or to an even larger symmetry group such as O(N) with $N\geq 2$. In this paper
we are concerned with the technical details of series computations to allow for
a nontrivial vacuum expectation value $<\rho(x)>\not=0$, which is typical for
models that break a global ${\bf Z}_2$ symmetry. Examples are scalar fields
coupled to an external field, or manifestly gauge invariant effective models of
Higgs field condensates in the electroweak theory, even in the high temperature
phase. A nonvanishing tadpole implies an enormous proliferation of graphs and
limits the graphical series computation to the 10th order. To achieve the
hopping parameter series to comparable order as in the ${\bf Z}_2$ symmetric
case, the graphical expansion is replaced by an expansion into new algebraic
objects called vertex structures. In this way the 18th order becomes feasible.


title: Scaling of the Upsilon Spectrum in Lattice NRQCD

abstract:
  We present results for the spectrum of b-bbar bound states in the quenched
approximation for three different values of the lattice spacing, in the range
0.05fm to 0.15fm. We find our results for spin-independent splittings in
physical units to be independent of the lattice spacing, indicating the absence
of systematic errors from discretisation effects. Spin-dependent splittings are
more sensitive to the lattice spacing and higher order corrections to the
action; we discuss the size of these effects and what can be done to arrive at
a physical result.


title: New results on heavy hadron spectroscopy with NRQCD

abstract:
  We present results for the spectrum of b-bbar bound states in the quenched
approximation for three different values of the lattice spacing. Results for
spin-independent splittings are shown to have good scaling behaviour;
spin-dependent splittings are more sensitive to discretisation effects. We
discuss what needs to be done to match the experimental spectrum.


title: Issues for the Lattice in Hadron Spectroscopy

abstract:
  Lattice QCD predicts a rich spectroscopy of glueballs and $q\bar{q}-$glue h
ybrids. I compare these with data and assess the emerging empirical situation.
Questions for the lattice are proposed.


title: Semileptonic Form Factors

abstract:
  I report the current status of the heavy-light decay constants, the bag
parameters and the semileptonic form factors. I compare the heavy-light decay
constants with Wilson-Wilson and clover-clover fermions. Systematic errors such
as scale setting and renormalization factors are also discussed. 1/M
dependences for the heavy-light semileptonic form factors near $q^2 = q^2_max$
with clover-clover and NRQCD-Wilson fermions are found to be small.


title: Gluon propagator and zero-momentum modes in SU(2) lattice gauge theory

abstract:
  We investigate propagators in Lorentz (or Landau) gauge by Monte Carlo
simulations. In order to be able to compare with perturbative calculations we
use large $\beta$ values. There the breaking of the Z(2) symmetry turns out to
be important for all of the four lattice directions. Therefore we make sure
that the analysis is performed in the correct state. We discus implications of
the gauge fixing mechanism and point out the form of the weak-coupling behavior
to be expected in the presence of zero-momentum modes. Our numerical result is
that the gluon propagator in the weak-coupling limit is strongly affected by
zero-momentum modes. This is corroborated in detail by our quantitative
comparison with analytical calculations.


title: Advanced Lattice QCD

abstract:
  The topics covered by the lectures include Symanzik's effective continuum
theory, O(a) improvement, chiral symmetry on the lattice and non-perturbative
renormalization.


title: Thermodynamics using Wilson and Staggered Quarks

abstract:
  Recent developements in QCD at finite temperature are reviewed. Particular
emphasis is laid on results stemming from simulations which involve quarks.


title:
Spatial string tension in gluodynamics at finite temperature in a
  spherical model approximation

abstract:
  Spatial string tension is computed in finite temperature gluodynamics on
asymmetric lattices in a spherical model approximation. Conditions of scaling
behavior are specified. Discrepancies with a standard renormalisation procedure
are discussed.


title: Monopoles in QCD

abstract:
  Based on the dual Higgs picture for confinement, we study monopole properties
in the maximally abelian (MA) gauge using the lattice QCD. The monopole carries
a large fluctuation of the gluon field and provides a large abelian action in
abelian projected QCD (AP-QCD). We find large cancellation between abelian part
and off-diagonal part of the action density around the monopole, which ensures
the appearance of monopoles. The monopole in the MA gauge can be regarded as
the collective mode of the large gluon fluctuation concentrated into the
abelian sector, and would be relevant degrees of freedom for confinement in
AP-QCD.


title: Geometrical aspects of chiral anomalies in the overlap

abstract:
  The set of one dimensional lowest energy eigenspaces used to construct the
overlap induces a two form on gauge orbit space which is the locally exact curl
of Berry's connection. If anomalies do not cancel, examples of two dimensional
closed sub-manifolds of orbit space are produced over which the integral of the
above two form does not vanish. Based on these observations, a natural
definition of covariant currents is obtained, a simple way to calculate chiral
anomalies on the lattice is found, and indications for how to construct an
ideal regularization of chiral gauge theories are seen to emerge.


title:
Perturbative Renormalization Factors of Bilinear Quark Operators for
  Improved Gluon and Quark Actions in Lattice QCD

abstract:
  We calculate one-loop renormalization factors of bilinear quark operators for
gluon action including six-link loops and $O(a)$-improved quark action in the
limit of massless quark. We find that finite parts of one-loop coefficients of
renormalization factors diminish monotonically as either of the coefficients
$c_1$ or $c_2+c_3$ of the six-link terms are decreased below zero. Detailed
numerical results are given, for general values of the clover coefficient, for
the tree-level improved gluon action in the Symanzik approach $(c_1=-1/12,
c_2=c_3=0)$ and for the choices suggested by Wilson $(c_1=-0.252, c_2=0,
c_3=-0.17)$ and by Iwasaki $(c_1=-0.331, c_2=c_3=0$ and $c_1=-0.27,
c_2+c_3=-0.04)$ from renormalization-group analyses. Compared with the case of
the standard plaquette gluon action, finite parts of one-loop coefficients are
reduced by 10--20% for the Symanzik action, and approximately by a factor two
for the renormalization-group improved gluon actions.


title: Monopole Loop Distribution and Confinement in SU(2) Lattice Gauge Theory

abstract:
  The abelian-projected monopole loop distribution is extracted from maximal
abelian gauge simulations. The number of loops of a given length falls as a
power of the length nearly independent of lattice size. This power increases
with $\beta=4/g^2$, reaching five around $\beta=2.85$, beyond which loops any
finite fraction of the lattice size vanish in the infinite lattice limit,
suggesting the continuum theory lacks confinement.


title: Monopoles in the Abelian Projection of Gluodynamics

abstract:
  We discuss some properties of the abelian monopoles in compact U(1) gauge
theory and in the SU(2) gluodynamics both on the lattice and in the continuum.


title: Dynamical Flavour Symmetry Breaking by a Magnetic Field in Lattice QED_3

abstract:
  We perform a lattice study, in the quenched approximation, of dynamical mass
generation in a system of relativistic (Dirac) fermions, coupled to an Abelian
gauge field in (2+1)-dimensions, in the presence of an external (constant)
magnetic field, perpendicular to the spatial planes. It is shown that a strong
magnetic field catalyzes chiral symmetry breaking, in agreement with results in
the continuum. The r\^ole of the higher-Landau poles in inducing a critical
temperature above which the phenomenon disappears is pointed out. We also
discuss the implications of this model on the opening of a gap in doped
antiferromagnetic superconductors.


title: Tadpole renormalization and relativistic corrections in lattice NRQCD

abstract:
  We make a comparison of two tadpole renormalization schemes in the context of
the quarkonium hyperfine splittings in lattice NRQCD. Improved gauge-field and
NRQCD actions are analyzed using the mean-link $u_{0,L}$ in Landau gauge, and
using the fourth root of the average plaquette $u_{0,P}$. Simulations are done
for $c\bar c$, $b\bar c$, and $b\bar b$ systems. The hyperfine splittings are
computed both at leading and at next-to-leading order in the relativistic
expansion. Results are obtained at lattice spacings in the range of about
0.14~fm to 0.38~fm. A number of features emerge, all of which favor tadpole
renormalization using $u_{0,L}$. This includes much better scaling behavior of
the hyperfine splittings in the three quarkonium systems when $u_{0,L}$ is
used. We also find that relativistic corrections to the spin splittings are
smaller when $u_{0,L}$ is used, particularly for the $c\bar c$ and $b\bar c$
systems. We also see signs of a breakdown in the NRQCD expansion when the bare
quark mass falls below about one in lattice units. Simulations with $u_{0,L}$
also appear to be better behaved in this context: the bare quark masses turn
out to be larger when $u_{0,L}$ is used, compared to when $u_{0,P}$ is used on
lattices with comparable spacings. These results also demonstrate the need to
go beyond tree-level tadpole improvement for precision simulations.


title: Abelian Projection without Ambiguities

abstract:
  Laplacian Abelian Projection is discussed. This term refers to the use of a
new (``Laplacian'') gauge fixing prescription for implementing the Abelian
Projection of QCD. The gauge condition is based on the lowest-lying eigenvector
of the covariant Laplacian operator in the adjoint representation.
  This Laplacian gauge fixing procedure is free of the ambiguities which plague
lattice simulations which work with the popular Maximally Abelian Gauge.
Furthermore, Laplacian gauge fixed configurations enjoy a natural kind of
smoothness. These two properties are crucial for a reliable determination of
physical quantities using the Abelian Projection.
  We also examine a new, Higgs-field-like observable which emerges as a
by-product of the method. This quantity can be used to identify magnetic
monopoles in a way independent of the traditional prescription. It is argued
that physically relevant magnetic monopoles are accomodated well by the
Laplacian method, while they are suppressed (too) strongly in Maximally Abelian
Gauge.
  Finally, first evidence of abelian dominance in the Laplacian Abelian
Projection is presented.


title: Extension of the Nielsen-Ninomiya theorem

abstract:
  The index theorem is employed to extend the no-go theorem for lattice chiral
Dirac fermions to translation non-invariant and non-local formulations.


title: Hadronic Molecules in Lattice QCD

abstract:
  An adiabatic approximation is used to derive the binding potential between
two heavy-light mesons in quenched SU(2)-colour lattice QCD. Analysis of the
meson-meson system shows that the potential is attractive at short- and
medium-range. The numerical data is consistent with the Yukawa model of pion
exchange


title: O(1/M^3) effects for heavy-light mesons in lattice NRQCD

abstract:
  The masses of spin-singlet and spin-triplet S-wave mesons containing a single
heavy quark are computed in the quenched approximation. The light quark action
and gauge field action are both classically-improved and tadpole-improved, and
the couplings to the heavy quark are organized by the 1/M expansion of
tadpole-improved NRQCD. At each of two lattice spacings, near 0.22fm and
0.26fm, meson masses are obtained for heavy quarks spanning the region between
charmed and bottom mesons. Results up to O(1/M), O(1/M^2) and O(1/M^3) are
displayed separately, so that the convergence of the heavy quark expansion can
be discussed. Also, the effect of each term in the O(1/M^3) contribution is
computed individually. For bottom mesons the 1/M-expansion appears to be
satisfactory, but the situation for charmed mesons is less clear.


title:
A First Principles Estimate of Finite Size Effects in Quark-Gluon Plasma
  Formation

abstract:
  Using lattice simulations of quenched QCD we estimate the finite size effects
present when a gluon plasma equilibrates in a slab geometry, i.e., finite width
but large transverse dimensions. Significant differences are observed in the
free energy density for the slab when compared with bulk behavior. A small
shift in the critical temperature is also seen. The free energy required to
liberate heavy quarks relative to bulk is measured using Polyakov loops; the
additional free energy required is on the order of 30-40 MeV at 2-3 T_c.


title: Heavy Quarks on the Lattice

abstract:
  This lecture describes the treatment of heavy quarks in lattice QCD by
implementing the Isgur-Wise limit. The method is briefly discussed, and some of
the special features of the resulting theory are highlighted. We emphasize
issues of the renormalization of the effective theory. The formulation permits
a calculation of heavy quark processes even when the momentum transfers are
much larger than the inverse lattice spacing. Applications include
semi-leptonic heavy quark decay and scattering processes, including the
computation of the nonperturbative part of the Isgur-Wise universal function.


title:
A study of the phase transition in 4D pure compact U(1) LGT on toroidal
  and spherical lattices

abstract:
  We have performed a systematic study of the phase transition in the pure
compact U(1) lattice gauge theory in the extended coupling parameter space
(\beta, \gamma) on toroidal and spherical lattices. The observation of a
non-zero latent heat in both topologies for all investigated \gamma in the
interval [+0.2,-0.4], together with an effective exponent \nu = 1/d when large
enough lattices are considered, lead us to conclude that the phase transition
is first order. For negative \gamma, our results point to an increasingly weak
first order transition as \gamma is made more negative.


title:
Scanning the Topological Sectors of the QCD Vacuum with Hybrid Monte
  Carlo

abstract:
  We address a long standing issue and determine the decorrelation efficiency
of the Hybrid Monte Carlo algorithm (HMC), for full QCD with Wilson fermions,
with respect to vacuum topology. On the basis of five state-of-the art QCD
vacuum field ensembles (with 3000 to 5000 trajectories each and
m_pi/m_rho-ratios in the regime >0.56, for two sea quark flavours) we are able
to establish, for the first time, that HMC provides sufficient tunneling
between the different topological sectors of QCD. This will have an important
bearing on the prospect to determine, by lattice techniques, the topological
susceptibility of the vacuum, and topology sensitive quantities like the spin
content of the proton, or the eta' mass.


title: Messages for QCD from the Superworld

abstract:
  Recent discoveries in supersymmetric gauge theories have significant
implications for our understanding for QCD and of field theory in general. The
phases of N=1 supersymmetric QCD (SQCD) are discussed, and the possibility of
similar phases in non-supersymmetric QCD is emphasized. It is described how
duality in SQCD links many previously known duality transformations that were
thought to be distinct, including Olive-Montonen duality of N=4 supersymmetric
gauge theory and quark-hadron duality in (S)QCD. A link between Olive-Montonen
duality and the confining strings of (S)QCD is explained, in which a picture of
confinement via non-abelian monopole condensation --- a generalized dual
Meissner effect --- emerges explicitly. In this picture, unlike previous ones,
the confining flux tubes carry the correct Z_N discrete charges. A number of
studies of these subjects, which could be carried out using lattice gauge
theory, are proposed.


title: The Anisotropic Wilson Gauge Action

abstract:
  Anisotropic lattices, with a temporal lattice spacing smaller than the
spatial one, allow precision Monte Carlo calculations of problems that are
difficult to study otherwise: heavy quarks, glueballs, hybrids, and high
temperature thermodynamics, for example. We here perform the first step
required for such studies with the (quenched) Wilson gauge action, namely, the
determination of the renormalized anisotropy $\xi$ as a function of the bare
anisotropy $\xi_0$ and the coupling. By, essentially, comparing the
finite-volume heavy quark potential where the quarks are separated along a
spatial direction with that where they are separated along the time direction,
we determine the relation between $\xi$ and $\xi_0$ to a fraction of 1% for
weak and to 1% for strong coupling. We present a simple parameterization of
this relation for $1\leq \xi \leq 6$ and $5.5 \leq \beta \leq \infty$, which
incorporates the known one-loop result and reproduces our non-perturbative
determinations within errors. Besides solving the problem of how to choose the
bare anisotropies if one wants to take the continuum limit at fixed
renormalized anisotropy, this parameterization also yields accurate estimates
of the derivative $\partial\xi_0/\partial\xi$ needed in thermodynamic studies.


title: Explicitly real form of the Wilson-Dirac matrix for SU(2)

abstract:
  The Wilson-Dirac matrix for SU(2) with I=1/2 fermions is written in an
explicitly real form. The basis change relating it to the conventional form in
which the matrix has complex entries is also given. Some applications are
presented.


title: A Quark-Antiquark Condensate in Three-Dimensional QCD

abstract:
  Three-dimensional lattice QCD is studied by Monte Carlo simulations within
the quenched approximation. At zero temperature a quark-antiquark condensate is
observed in the limit of vanishing quark masses. The condensate vanishes
continuously at the finite-temperature deconfinement phase transition of the
theory. A natural interpretation of this phenomenon in the full theory with
dynamical quarks is in terms of the spontaneous flavor symmetry breaking
$U(N_f) \to U(N_f/2)\times U(N_f/2)$. In addition, the spectrum of low-lying
Dirac operator eigenvalues is computed and found to be consistent with a flat
distribution at zero temperature, in agreement with analytical predictions.


title: Lattice Investigation of the DMO Sum Rule

abstract:
  An evaluation of charged pion polarizability using correlation functions
measured on a 16^{3}\times 24 lattice in the context of the Das, Mathur, Okubo
(DMO) sum rule is carried out. The calculation is limited to the so-called
intrinsic part of the polarizability. This contribution, equivalent to a
Euclidean time integral over vector and axial vector momentum-differentiated
propagators, is evaluated in both a continuous and discrete sense. In the
continuous case, the time behavior of the correlation functions is fit to the
continuum quark model; the discrete case is handled by a straightforward
application of Simpson's rule for integration after subtracting the pion
contributions. A comparison of the implied vector meson and pion decay
constants with phenomenological values is carried out. Results for the
intrinsic polarizability are extrapolated across four quark mass values to the
chiral limit. An extensive discussion of the lattice systematics in this
calculation is given.


title: Fixed point actions and on-shell tree-level Symanzik improvement

abstract:
  In this paper it is argued that the properties of the fixed point action of a
renormalization group transformation can be used to implement the on-shell
tree-level Symanzik improvement of lattice actions to any given order in the
expansion in the lattice spacing, in a way which does not involve any
perturbative calculations. In particular, a well-known technique for the lowest
order improvement of SU(N) lattice gauge theories is revisited from the point
of view of fixed point actions, which allows to shed light on some subtle
points.


title: Gluon Propagator in the Infrared Region

abstract:
  The gluon propagator is calculated in quenched QCD for two different lattice
sizes (16^3x48 and 32^3x64) at beta=6.0. The volume dependence of the
propagator in Landau gauge is studied. The smaller lattice is instrumental in
revealing finite volume and anisotropic lattice artefacts. Methods for
minimising these artefacts are developed and applied to the larger lattice
data. New structure seen in the infrared region survives these conservative
cuts to the lattice data. This structure serves to rule out a number of models
that have appeared in the literature. A fit to a simple analytical form
capturing the momentum dependence of the nonperturbative gluon propagator is
also reported.


title: Overlap formula for the chiral multiplet

abstract:
  The vacuum overlap formalism is extended to describe the supersymmetric
multiplet of a Weyl fermion, a complex scalar boson and an auxiliary field in
the case without interaction, based on the fact that supersymmetry can be
maintained upto quadratic terms by introducing bosonic species doublers. We
also obtain a local action which describes the chiral multiplet and discuss its
symmetry structure. It is shown that, besides the manifest supersymmetry, the
action possesses a chiral symmetry of the type given by L\"uscher and analogous
bosonic symmetries which may be regarded as independent infinitesimal rotations
of complex phases of the scalar and the auxiliary fields. This implies that the
$U(1) \times U(1)_R$ symmetry of the chiral multiplet can be exact on the
lattice.


title: O(a) improvement of lattice QCD with two flavors of Wilson quarks

abstract:
  We consider O(a) improvement for two flavor lattice QCD. The improvement term
in the action is computed non-perturbatively for a large range of the bare
coupling. The position of the critical line and higher order lattice artifacts
remaining after improvement are estimated. We also discuss the behavior of the
HMC algorithm in our simulations.


title: Truncated Perfect Actions for Staggered Fermions

abstract:
  We discuss the behavior of free perfect staggered fermions and truncated
versions thereof. The study includes flavor non-degenerate masses. We suggest a
new blocking scheme, which provides excellent locality of the perfect lattice
action. A truncation procedure adequate for the structure of staggered fermions
is applied. We consider spectral and thermodynamic properties and compare
truncated perfect actions, Symanzik improved and standard staggered fermions in
two and four dimensions.


title: Scaling in a toy model of gluodynamics at finite temperatures

abstract:
  In the limit of $\xi \simeq a_\sigma /a_\tau \to \infty $ the gluodynamics
without the magnetic part of action ($S_M\sim 1/\xi $) is considered as a
self-contained model. The model is studied analytically in the continuum limit
on an extremely large lattice ($N_\tau \to \infty $). Scaling conditions for
critical temperature and string tension are considered. The model shows trivial
($g^2\sim a_\tau $) asymptotic freedom in the case of continuous gauge groups
and nontrivial one ($g^2\sim 1/\ln 1/a_\tau $) for discrete groups.


title: Monopoles and hadron spectrum in quenched QCD

abstract:
  We study quenched hadron spectra with Wilson fermion in abelian gauge fields
extracted by maximal abelian projection and in fields induced by monopoles on
$16^3 \times 32 $ and $ 12^3 \times 24$ lattices. Pion mass squared and quark
mass defined through the axial Ward identity satisfy the PCAC relation. Gross
features of the light hadron spectra are almost similar to those in SU(3) gauge
fields if normalization is made by the square root of the string tension. It is
also shown that no sizable dynamical mass generation is found in the present
range of $\kappa$ when the monopole degree of freedom is removed from the
abelian fields or from the SU(3) gauge fields.


title:
On the Definition of Gauge Field Operators in Lattice Gauge-Fixed
  Theories

abstract:
  We address the problem of defining the gauge four-potential on the lattice,
in terms of the natural link variables. Different regularized definitions are
shown, through non perturbative numerical computation, to converge towards the
same continuum renormalized limit.


title:
Investigation of a Toy Model for Frustration in Abelian Lattice Gauge
  Theory

abstract:
  We introduce a lattice model with local U(1) gauge symmetry which
incorporates explicit frustration in d >2. The form of the action is inspired
from the loop expansion of the fermionic determinant in standard lattice QED.
We study through numerical simulations the phase diagram of the model,
revealing the existence of a frustrated (antiferromagnetic) phase for d=3 and
d=4, once an appropriate order parameter is identified.


title:
Solutions of the Ginsparg-Wilson relation and improved domain wall
  fermions

abstract:
  We discuss a number of lattice fermion actions solving the Ginsparg-Wilson
relation. We also consider short ranged approximate solutions. In particular,
we are interested in reducing the lattice artifacts, while avoiding (or
suppressing) additive mass renormalization. In this context, we also arrive at
a formulation of improved domain wall fermions.


title: Tadpole-improved SU(2) lattice gauge theory

abstract:
  A comprehensive analysis of tadpole-improved SU(2) lattice gauge theory is
made. Simulations are done on isotropic and anisotropic lattices, with and
without improvement. Two tadpole renormalization schemes are employed, one
using average plaquettes, the other using mean links in Landau gauge.
Simulations are done with spatial lattice spacings $a_s$ in the range of about
0.1--0.4 fm. Results are presented for the static quark potential, the
renormalized lattice anisotropy $a_t/a_s$ (where $a_t$ is the ``temporal''
lattice spacing), and for the scalar and tensor glueball masses. Tadpole
improvement significantly reduces discretization errors in the static quark
potential and in the scalar glueball mass, and results in very little
renormalization of the bare anisotropy that is input to the action. We also
find that tadpole improvement using mean links in Landau gauge results in
smaller discretization errors in the scalar glueball mass (as well as in the
static quark potential), compared to when average plaquettes are used. The
possibility is also raised that further improvement in the scalar glueball mass
may result when the coefficients of the operators which correct for
discretization errors in the action are computed beyond tree level.


title: Lattice Gauge Fixing, Gribov Copies and BRST Symmetry

abstract:
  We show that a modification of the BRST lattice quantization allows to
circumvent an old paradox, formulated by Neuberger, related to lattice Gribov
copies and non-perturbative BRST invariance. In the continuum limit the usual
BRST formulation is recovered.


title: A New Look at the Axial Anomaly in Lattice QED with Wilson Fermions

abstract:
  By carrying out a systematic expansion of Feynman integrals in the lattice
spacing, we show that the axial anomaly in the U(1) lattice gauge theory with
Wilson fermions, as determined in one-loop order from an irrelevant lattice
operator in the Ward identity, must necessarily be identical to that computed
from the dimensionally regulated continuum Feynman integrals for the triangle
diagrams.


title: The theoretical background and properties of perfect actions

abstract:
  This lecture note starts with a pedagogical introduction to the theoretical
background and properties of perfect actions, gives some details on topology
and instanton solutions and ends with a discussion on the recent developments
concerning chiral symmetry.


title: More on Lattice BRST Invariance

abstract:
  In the gauge-fixing approach to (chiral) lattice gauge theories, the action
in the U(1) case implicitly contains a free ghost term, in accordance with the
continuum abelian theory. On the lattice there is no BRST symmetry and, without
fermions, the partition function is strictly positive. Recently, Neuberger
pointed out in hep-lat/9801029 that a different choice of the ghost term would
lead to a BRST-invariant lattice model, which is ill-defined nonperturbatively.
We show that such a lattice model is inconsistent already in perturbation
theory, and clearly different from the gauge-fixing approach.


title:
Corrections to Finite-Size Scaling in the Lattice N-Vector Model for
  Infinite N

abstract:
  We compute the corrections to finite-size scaling for the N-vector model on
the square lattice in the large-N limit. We find that corrections behave as log
L/L^2. For tree-level improved hamiltonians corrections behave as 1/L^2. In
general l-loop improvement is expected to reduce this behaviour to 1/(L^2
\log^l L). We show that the finite-size-scaling and the perturbative limit do
not commute in the calculation of the corrections to finite-size scaling. We
present also a detailed study of the corrections for the RP^N-model.


title: Strings and Aharonov-Bohm Effect in Abelian Higgs Model

abstract:
  We investigate numerically the properties of the Abrikosov-Nielsen-Olesen
strings in 4D abelian Higgs model. The fractal dimension D_f of the vortex
strings was found to be large in the Coulomb phase and it is close to 2 in the
Higgs phase. We also show that the Wilson loop for non-integer charges is
correlated with the linking number of the vortex string world sheets and the
test particle world trajectory. We find that this topological (Aharonov-Bohm)
interaction gives the main contribution to the Wilson loop quantum average for
non-integer test charges in the vicinity of the Coulomb-Higgs phase transition.


title: An interquark potential model for multi-quark systems

abstract:
  A potential model for four interacting quarks is constructed in SU(2) from
six basis states -- the three partitions into quark pairs, where the gluon
field is either in its ground state or first excited state. With four
independent parameters to describe the interactions connecting these basis
states, it is possible to fit 100 pieces of data -- the ground and first
excited states of configurations from six different four-quark geometries
calculated on a 16^3*32 lattice.


title: Four-quark flux distribution and binding in lattice SU(2)

abstract:
  The full spatial distribution of the color fields of two and four static
quarks is measured in lattice SU(2) field theory at separations up to 1 fm at
beta=2.4. The four-quark case is equivalent to a qbar q qbar q system in SU(2)
and is relevant to meson-meson interactions. By subtracting two-body flux tubes
from the four-quark distribution we isolate the flux contribution connected
with the four-body binding energy. This contribution is further studied using a
model for the binding energies. Lattice sum rules for two and four quarks are
used to verify the results.


title: Quantum Chromodynamics with Many Flavors

abstract:
  We investigate the phase structure of lattice QCD for general number of
flavors $N_F$. Based on numerical data combined with the results of the
perturbation theory we propose the following picture: When $N_F \ge 17$, there
is only one IR fixed point at vanishing gauge coupling, i.e., 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. 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:
An Introduction to Finite Temperature Quantum Chromodynamics on the
  Lattice

abstract:
  In these lectures, we introduce finite temperature QCD on the lattice to
non-experts of the subject. We first formulate lattice QCD both at zero and
finite temperatures. Then a section is devoted to the topic of improved lattice
actions which are becoming an essential ingredient of precision studies of QCD
on the lattice. We then discuss about finite temperature SU(3) gauge theory,
i.e. QCD without dynamical quarks (quenched QCD). Finally, we report recent
status of studies in full QCD taking into account the effects of dynamical
quarks.


title: Comparison of Improved and Unimproved Quenched Hadron Spectroscopy

abstract:
  We make a comparison between our quenched-hadron-spectroscopy results for the
non-perturbatively-improved Wilson action and the corresponding unimproved
case, at beta=6.2 on the same set of gauge configurations. Within our
statistics, we find a sizeable improvement for the baryon spectrum and for the
determination of the strange-quark mass.


title: SU(N) gauge theories in 2+1 dimensions

abstract:
  We calculate the mass spectra and string tensions of SU(2), SU(3), SU(4) and
SU(5) gauge theories in 2+1 dimensions. We do so by simulating the
corresponding lattice theories and then extrapolating dimensionless mass ratios
to the continuum limit. We find that such mass ratios are, to a first
approximation, independent of the number of colours and that the remaining
dependence can be accurately reproduced by a simple O(1/N.N) correction. This
provides us with a prediction of these mass ratios for all SU(N) theories in
2+1 dimensions and demonstrates that these theories are already `close' to
N=infinity for N=2. We find that the theory retains a non-zero confining string
tension as N goes to infinity and that the dimensionful coupling g.g is
proportional to 1/N at large N, when expressed in units of the dynamical length
scale of the theory. During the course of these calculations we study in detail
the effects of including over-relaxation in the Monte Carlo, of using a
mean-field improved coupling to extrapolate to the continuum limit, and the use
of space-time asymmetric lattice actions to resolve heavy glueball correlators.


title:
On the Deconfinement Phase Transition in Hot Gauge Theories with
  Dynamical Matter Fields

abstract:
  The phase structure of hot gauge theories with dynamical matter fields is
reexamined in the canonical ensemble with respect to triality. Since this
ensemble implies a projection to the zero triality sector of the theory we
introduce a proper quantity which is able to reveal a critical behaviour of the
theory with fundamental quarks. We discuss the properties of both the
chromoelectric and chromomagnetic sectors of the theory and show while electric
charges carrying a unit of Z(N) charge are screened at high temperatures by
dynamical matter loops, this is not the case for the Z(N) magnetic flux. An
order parameter is constructed to probe the realization of local discrete Z(N)
symmetry in the magnetic sector. We argue it can be used to detect a
deconfinement phase being defined in terms of the screening mechanism as a
phase of unscreened Z(N) flux. It may be detectable at long range via the
Aharonov-Bohm effect. We discuss the possible phase structure of QCD in this
approach.


title: Simulation of Supersymmetric Models with a Local Nicolai Map

abstract:
  We study the numerical simulation of supersymmetric models having a local
Nicolai map. The mapping can be regarded as a stochastic equation and its
numerical integration provides an algorithm for the simulation of the original
model. In this paper, the method is discussed in details and applied to
examples in 0+1 and 1+1 dimensions.


title:
4d Simplicial Quantum Gravity: Matter Fields and the Corresponding
  Effective Action

abstract:
  Four-dimensional simplicial quantum gravity is modified either by coupling it
to U(1) gauge fields or by introducing a measure weighted by the orders of the
triangles. Strong coupling expansion and Monte Carlo simulations are used.
Although the two modifications of the standard pure-gravity model are
apparently very distinct, they produce strikingly similar results, as far as
the geometry of random manifolds is concerned. In particular, for an
appropriate choice of couplings, the branched polymer phase is replaced by a
crinkled phase, characterized by the susceptibility exponent $\gamma < 0$ and
the fractal dimension $d_H > 2$. The quasi-equivalence between the two models
is exploited to get further insight into the extended phase diagram of the
theory.


title: Chiral properties of the fixed point action of the Schwinger model

abstract:
  We study the spectrum properties for a recently constructed fixed point
lattice Dirac operator. We also consider the problem of the extraction of the
fermion condensate, both by direct computation, and through the Banks-Casher
formula by analyzing the density of eigenvalues of a redefined antihermitean
lattice Dirac operator.


title: Improved Error Estimate for the Valence Approximation

abstract:
  We construct a systematic mean-field-improved coupling constant and quark
loop expansion for corrections to the valence (quenched) approximation to
vacuum expectation values in the lattice formulation of QCD. Terms in the
expansion are evaluated by a combination of weak coupling perturbation theory
and a Monte Carlo algorithm.


title:
Analytical study of fermion determinant and chiral condensate behavior
  at finite temperatures in toy model approximation

abstract:
  Fermion determinant is computed analytically on extremely large lattices $%
N_\tau \to \infty $ in the toy model approximation in which action is truncated
so that in the Hamiltonian limit of $a_\tau \to 0$ all terms of order $a_\tau
/a_\sigma $ are discarded$.$ Chiral condensate is studied in the area of small
($m<<T$) quark masses.


title: Gauge-fixing approach to lattice chiral gauge theories

abstract:
  We review the status of our recent work on the gauge-fixing approach to
lattice chiral gauge theories. New numerical results in the reduced version of
a model with a U(1) gauge symmetry are presented which strongly indicate that
the factorization of the correlation functions of the left-handed neutral and
right-handed charged fermion fields, which we established before in
perturbation theory, holds also nonperturbatively.


title:
Topological Charge and The Spectrum of Exactly Massless Fermions on the
  Lattice

abstract:
  The square root of the positive definite hermitian operator $D_w^{\dagger}
D_w$ in Neuberger's proposal of exactly massless quarks on the lattice is
implemented by the recursion formula $Y_{k+1} = {1/2} (Y_k + D_w^{\dagger} D_w
Y_k^{-1})$ with $Y_0 = \Id$, where $Y_k^2$ converges to $D_w^{\dagger} D_w$
quadratically. The spectrum of the lattice Dirac operator for single massless
fermion in two dimensional background U(1) gauge fields is investigated. For
smooth background gauge fields with non-zero topological charge, the exact zero
modes with definite chirality are reproduced to a very high precision on a
finite lattice and the Index Theorem is satisfied exactly. The fermionic
determinants are also computed and they are in good agreement with the
continuum exact solution.


title: Understanding Hadron Structure Using Lattice QCD

abstract:
  An elementary introduction is presented to the study of hadron structure
using lattice QCD. Following a brief review of relevant aspects of path
integrals, the discrete lattice path integral is presented for gluon and quark
fields and used to calculate physical observables. Essential aspects of
instanton physics are reviewed, and it is shown how the instanton content is
extracted from lattice gluon configurations. Finally, both comparison of
results including all gluons with those including only instantons and the study
of quark zero modes associated with instantons and their contributions to
hadronic observables are used to show the dominant role of gluons in hadron
structure.


title:
Dynamical Linked Cluster Expansions: A Novel Expansion Scheme for
  Point-Link-Point-Interactions

abstract:
  Dynamical linked cluster expansions are linked cluster expansions with
hopping parameter terms endowed with their own dynamics. This amounts to a
generalization from 2-point to point-link-point interactions. We develop an
associated graph theory with a generalized notion of connectivity and describe
an algorithmic generation of the new multiple-line graphs. We indicate physical
applications to spin glasses, partially annealed neural networks and SU(N)
gauge Higgs systems. In particular the new expansion technique provides the
possibility of avoiding the replica-trick in spin glasses. We consider
variational estimates for the SU(2) Higgs model of the electroweak phase
transition. The results for the transition line, obtained by dynamical linked
cluster expansions, agree quite well with corresponding high precision Monte
Carlo results.


title: The MSSM Electroweak Phase Transition on the Lattice

abstract:
  We study the MSSM finite temperature electroweak phase transition with
lattice Monte Carlo simulations, for a large Higgs mass (m_H ~ 95 GeV) and
light stop masses (m_tR ~ 150...160 GeV). We employ a 3d effective field theory
approach, where the degrees of freedom appearing in the action are the SU(2)
and SU(3) gauge fields, the weakly interacting Higgs doublet, and the strongly
interacting stop triplet. We determine the phase diagram, the critical
temperatures, the scalar field expectation values, the latent heat, the
interface tension and the correlation lengths at the phase transition points.
Extrapolating the results to the infinite volume and continuum limits, we find
that the transition is stronger than indicated by 2-loop perturbation theory,
guaranteeing that the MSSM phase transition is strong enough for baryogenesis
in this regime. We also study the possibility of a two-stage phase transition,
in which the stop field gets an expectation value in an intermediate phase. We
find that a two-stage transition exists non-perturbatively, as well, but for
somewhat smaller stop masses than in perturbation theory. Finally, the latter
stage of the two-stage transition is found to be extremely strong, and thus it
might not be allowed in the cosmological environment.


title: Frustration in Finite Density QCD

abstract:
  We present a detailed analysis of the QCD partition function in the Grand
Canonical formalism. Using the fugacity expansion we find evidence for
numerical instabilities in the standard evaluation of its coefficients. We
discuss the origin of this problem and propose an issue to it. The correct
analysis shows no evidence for a discontinuity in the baryonic density in the
strong coupling limit. The moderate optimism that was inspired by the Grand
Canonical Partition Function calculations in the last years has to be
considered ill-founded.


title: The standard model and the lattice

abstract:
  I discuss some of the difficulties with formulating chiral symmetry on the
lattice and review a recently proposed scheme for a fully finite and exactly
gauge invariant lattice regularization of the standard model.


title: Center Disorder in the 3D Georgi-Glashow Model

abstract:
  We present a number of arguments relating magnetic disorder to center
disorder, in pure Yang-Mills theory in D=3 and D=4 dimensions. In the case of
the D=3 Georgi-Glashow model, we point out that the abelian field distribution
is not adequatedly represented, at very large scales, by that of a monopole
Coulomb gas. The onset of center disorder is associated with the breakdown of
the Coulomb gas approximation; this scale is pushed off to infinity in the
QED_3 limit of the 3D Georgi-Glashow model, but should approach the
color-screening length in the pure Yang-Mills limit.


title: Diquark Masses from Lattice QCD

abstract:
  We present first results for diquark correlation functions calculated in
Landau gauge on the lattice. Masses have been extracted from the long distance
behaviour of these correlation functions. We find that the ordering of diquark
masses with spin 0 and 1 states in colour anti-triplet and sextet channels is
in accordance with instanton motivated interaction models. Although we find
evidence for an attractive interaction in colour anti-triplet states with a
splitting between spin 0 and spin 1 diquarks that can account for the mass
splitting between the nucleon and the delta, there is no evidence for a deeply
bound diquark state.


title:
The Massive Schwinger Model - a Hamiltonian Lattice Study in a Fast
  Moving Frame

abstract:
  We present a non-perturbative study of the massive Schwinger model. We use a
Hamiltonian approach, based on a momentum lattice corresponding to a fast
moving reference frame, and equal time quantization. We present numerical
results for the mass spectrum of the vector and scalar particle. We find good
agreement with chiral perturbation theory in the strong coupling regime and
also with other non-perturbative studies (Hamer et al., Mo and Perry) in the
non-relativistic regime. The most important new result is the study of the
$\theta$-action, and computation of vector and scalar masses as a function of
the $\theta$-angle. We find excellent agreement with chiral perturbation
theory. Finally, we give results for the distribution functions. We compare our
results with Bergknoff's variational study from the infinite momentum frame in
the chiral region.


title: Confinement Physics and Topology in QCD

abstract:
  Based on the dual-superconductor picture, we study the confinement physics in
QCD in terms of the monopole in the maximally abelian (MA) gauge using the
SU(2) lattice QCD. In the MA gauge, the off-diagonal gluon component is forced
to be small, and hence microscopic abelian dominance on the link variable is
observed in the lattice QCD for the whole region of $\beta$. From the
gluon-propagator analysis in the lattice QCD, the origin of abelian dominance
for the long-range physics is interpreted as the effective mass $m_{ch} \simeq
0.9 {\rm GeV}$ of the charged gluon induced by the MA gauge fixing. In the MA
gauge, there appears the macroscopic network of the monopole world-line
covering the whole system, which would be identified as monopole condensation
at a large scale. Using the dual Wilson loop in the MA gauge, we find the
effective mass of the dual gluon field, $m_B \simeq $0.5GeV, which is the
evidence of the dual Higgs mechanism by monopole condensation. The large
fluctuation of off-diagonal gluons remains around the monopole in the MA gauge,
and this charged-gluon rich region would provide the effective monopole size as
the critical scale of the abelian projected QCD. Instantons are expected to
appear in the charged-gluon rich region around the monopole world-line in the
MA gauge, which leads to the local correlation between monopoles and
instantons.


title:
Perturbative and non-perturbative studies of the SU(2)-Higgs model on
  lattices with asymmetric lattice spacings

abstract:
  We present a calculation of the O(g^2,\lambda) perturbative corrections to
the coupling anisotropies of the SU(2)-Higgs model on lattices with asymmetric
lattice spacings. These corrections are obtained by a one-loop calculation
requiring the rotational invariance of the gauge and Higgs boson propagators in
the continuum limit. The coupling anisotropies are also determined from
numerical simulations of the model on appropriate lattices. The one-loop
perturbation theory and the simulation results agree with high accuracy. It is
demonstrated that rotational invariance is also restored for the static
potential determined from space-space and space-time Wilson loops.


title: Instantons and Monopoles in the Nonperturbative QCD

abstract:
  We study the confinement physics in QCD in the maximally abelian (MA) gauge
using the SU(2) lattice QCD. To clarify the origin of abelian dominance for the
long-range physics, we study the charged-gluon propagator in the lattice QCD,
and find that the effective mass $m_{ch} \simeq 0.9 {\rm GeV}$ of the charged
gluon is induced by the MA gauge fixing. In the MA gauge, there appears the
global network of the monopole world-line covering the whole system, which
would be identified as monopole condensation at a large scale. To prove
monopole condensation, we apply the dual gauge formalism to the monopole part,
and derive the inter-monopole potential from the dual Wilson loop in the MA
gauge. In the monopole part, which carries the nonperturbative aspects of QCD,
the dual gluon mass is evaluated as $m_B \simeq $0.5GeV, which is the evidence
of the dual Higgs mechanism by monopole condensation. As for the monopole
structure, the large fluctuation of off-diagonal gluons remains around the
monopole in the MA gauge, and large cancellation occurs between the diagonal
and off-diagonal action densities to keep the total QCD action finite. The
charged-gluon rich region around the QCD-monopole would provide the effective
monopole size as the critical scale of the abelian projected QCD. Instantons
are expected to appear in the charged-gluon rich region around the monopole
world-line in the MA gauge, which leads to the local correlation between
monopoles and instantons.


title: Spontaneous Flavor and Parity Breaking with Wilson Fermions

abstract:
  We discuss the phase diagram of Wilson fermions in the $m_0$--$g^2$ plane for
two-flavor QCD. We argue that, as originally suggested by Aoki, there is a
phase in which flavor and parity are spontaneously broken. Recent numerical
results on the spectrum of the overlap Hamiltonian have been interpreted as
evidence against Aoki's conjecture. We show that they are in fact consistent
with the presence of a flavor-parity broken ``Aoki phase''. We also show how,
as the continuum limit is approached, one can study the lattice theory using
the continuum chiral Lagrangian supplemented by additional terms proportional
to powers of the lattice spacing. We find that there are two possible phase
structures at non-zero lattice spacing: (1) there is an Aoki phase of width
$\Delta m_0 \sim a^3$ with two massless Goldstone pions; (2) there is no
symmetry breaking, and all three pions have an equal non-vanishing mass of
order $a$. Present numerical evidence suggests that the former option is
realized for Wilson fermions. Our analysis then predicts the form of the pion
masses and the flavor-parity breaking condensate within the Aoki phase. Our
analysis also applies for non-perturbatively improved Wilson fermions.


title: Improved Lattice Gauge Field Hamiltonian

abstract:
  Lepage's improvement scheme is a recent major progress in lattice $QCD$,
allowing to obtain continuum physics on very coarse lattices. Here we discuss
improvement in the Hamiltonian formulation, and we derive an improved
Hamiltonian from a lattice Lagrangian free of $O(a^2)$ errors. We do this by
the transfer matrix method, but we also show that the alternative via Legendre
transformation gives identical results. We consider classical improvement,
tadpole improvement and also the structure of L{\"u}scher-Weisz improvement.
The resulting color-electric energy is an infinite series, which is expected to
be rapidly convergent. For the purpose of practical calculations, we construct
a simpler improved Hamiltonian, which includes only nearest-neighbor
interactions.


title: Microscopic universality with dynamical fermions

abstract:
  It has recently been demonstrated in quenched lattice simulations that the
distribution of the low-lying eigenvalues of the QCD Dirac operator is
universal and described by random-matrix theory. We present first evidence that
this universality continues to hold in the presence of dynamical quarks. Data
from a lattice simulation with gauge group SU(2) and dynamical staggered
fermions are compared to the predictions of the chiral symplectic ensemble of
random-matrix theory with massive dynamical quarks. Good agreement is found in
this exploratory study. We also discuss implications of our results.


title: Towards a Topological Mechanism of Quark Confinement

abstract:
  We report on new analyses of the topological and chiral vacuum structure of
four-dimensional QCD on the lattice. Correlation functions as well as
visualization of monopole currents in the maximally Abelian gauge emphasize
their topological origin and gauge invariant characterization. The
(anti)selfdual character of strong vacuum fluctuations is reveiled by
smoothing. In full QCD, (anti)instanton positions are also centers of the local
chiral condensate and quark charge density. Most results turn out generically
independent of the action and the cooling/smoothing method.


title:
Strongly coupled lattice gauge theory with dynamical fermion mass
  generation in three dimensions

abstract:
  We investigate the critical behaviour of a three-dimensional lattice
$\chiU\phi_3$ model in the chiral limit. The model consists of a staggered
fermion field, a U(1) gauge field (with coupling parameter $\beta$) and a
complex scalar field (with hopping parameter $\kappa$). Two different methods
are used: 1) fits of the chiral condensate and the mass of the neutral
unconfined composite fermion to an equation of state and 2) finite size scaling
investigations of the Lee-Yang zeros of the partition function in the complex
fermion mass plane. For strong gauge coupling ($\beta < 1$) the critical
exponents for the chiral phase transition are determined. We find strong
indications that the chiral phase transition is in one universality class in
this $\beta$ interval: that of the three-dimensional Gross-Neveu model with two
fermions. Thus the continuum limit of the $\chiU\phi_3$ model defines here a
nonperturbatively renormalizable gauge theory with dynamical mass generation.
At weak gauge coupling and small $\kappa$, we explore a region in which the
mass in the neutral fermion channel is large but the chiral condensate on
finite lattices very small. If it does not vanish in the infinite volume limit,
then a continuum limit with massive unconfined fermion might be possible in
this region, too.


title:
High Temperature Behavior of the Chern-Simons Diffusion Rate in the 1+1
  D Abelian Higgs Model

abstract:
  We give arguments that in the 1+1 dimensional abelian Higgs model the
classical approximation can be good for the leading high temperature behavior
of real time processes. The Chern-Simons diffusion rate (`sphaleron rate') is
studied numerically in this approximation. New results at high temperature show
a $T^{2/3}$ behavior of the rate at sufficiently small lattice spacing.


title: Center vortices of Yang-Mills theory at finite temperatures

abstract:
  Recent lattice calculations performed at zero temperature and in the maximal
center gauge indicate that quark confinement can be understood in this gauge as
due to fluctuations in the number of magnetic vortices piercing a given Wilson
loop. This development has led to a revival of the vortex condensation theory
of confinement. For a SU(2) gauge group, we show that also at finite
temperatures, center vortices are the relevant collective infrared degrees of
freedom determining the long-range static quark potential; in particular, their
dynamics reflect the transition to the deconfining phase.


title:
Perturbative Thermodynamics of Lattice QCD with Chiral-Invariant
  Four-Fermion Interactions

abstract:
  Lattice QCD with additional chiral-invariant four-fermion interactions is
studied at nonzero temperature. Staggered Kogut-Susskind quarks are used. The
four-fermion interactions are implemented by introducing bosonic auxiliary
fields. A mean field treatment of the auxiliary fields is used to calculate the
model's asymptotic scale parameter and perturbative thermodynamics, including
the one-loop gluonic contributions to the energy, entropy, and pressure. In
this approach the calculations reduce to those of ordinary lattice QCD with
massive quarks. Hence, the previous calculations of these quantities in lattice
QCD using massless quarks are generalized to the massive case.


title:
Continuum limit of lattice QCD with staggered quarks in the quenched
  approximation - a critical role for the chiral extrapolation

abstract:
  We calculate the light quark spectrum of lattice QCD in the quenched
approximation using Kogut-Susskind quarks. By combining results for different
lattice spacings, several volumes and five quark masses, we are able to take
the light quark mass, infinite volume, continuum limit. When we use non-linear
chiral extrapolations, we find that the nucleon to rho mass ratio is 1.254 +-
0.018 +- 0.027, where the errors are statistical and systematic (within the
quenched approximation), respectively. This should be compared with the
experimental value of 1.22. Our results indicate that the error due to
quenching is less than about 5%.


title:
First lattice evidence for a non-trivial renormalization of the Higgs
  condensate

abstract:
  General arguments related to ``triviality'' predict that, in the broken phase
of $(\lambda\Phi^4)_4$ theory, the condensate $<\Phi>$ re-scales by a factor
$Z_{\phi}$ different from the conventional wavefunction-renormalization factor,
$Z_{prop}$. Using a lattice simulation in the Ising limit we measure
$Z_{\phi}=m^2 \chi$ from the physical mass and susceptibility and $Z_{prop}$
from the residue of the shifted-field propagator. We find that the two $Z$'s
differ, with the difference increasing rapidly as the continuum limit is
approached. Since $Z_{\phi}$ affects the relation of $<\Phi>$ to the Fermi
constant it can sizeably affect the present bounds on the Higgs mass.


title:
Studies in Random Geometries: Hypercubic Random Surfaces and Simplicial
  Quantum Gravity

abstract:
  We analyze two models of random geometries~: planar hyper-cubic random
surfaces and four dimensional simplicial quantum gravity.
  We show for the hyper-cubic random surface model that a geometrical
constraint does not change the critical properties of the model compared to the
model without this constraint. We analyze the phase diagram for the model with
extrinsic curvature.
  For four dimensional simplicial quantum gravity we find that in the large
volume limit the leading contribution to the entropy does not depend on the
underlying topology. We find for the first time a strong back-reaction of the
geometric sector for matter coupled to gravity.


title: Lattice Chiral Schwinger Model: Selected Results

abstract:
  We discuss a method for regularizing chiral gauge theories. The idea is to
formulate the gauge fields on the lattice, while the fermion determinant is
regularized and computed in the continuum. A simple effective action emerges
which lends itself to numerical simulations.


title:
Analysis of the Lee-Yang zeros in a dynamical mass generation model in
  three dimensions

abstract:
  We investigate a strongly U(1) gauge theory with fermions and scalars on a
three dimensional lattice and analyze whether the cintinuum limit might be a
renormalizable theory with dynamical mass generation. Most attention is paid to
the weak coupling region where a possible new dynamical mass generation
mechanism might exist. There we investigate the mass of the composite fermion,
the chiral condensate and the scaling of the Lee-Yang zeros.


title: Testing improved actions for dynamical Kogut-Susskind quarks

abstract:
  We extend tests of "Naik" and "fat link" improvements of the Kogut-Susskind
quark action to full QCD simulations, and verify that the improvements
previously demonstrated in the quenched approximation apply also to dynamical
quark simulations. We extend the study of flavor symmetry improvement to the
complete set of pions, and find that the nonlocal pions are significantly
heavier than the local non-Goldstone pion. These results can be used to
estimate the lattice spacing necessary for realistic simulations with this
action.


title: Noncompact, Gauge-Invariant Simulations of U(1), SU(2), and SU(3)

abstract:
  We have applied a new noncompact, gauge-invariant, Monte Carlo method to
simulate the U(1), SU(2), and SU(3) gauge theories on 8^4 and 12^4 lattices.
For U(1) the Creutz ratios of the Wilson loops agree with the exact results for
beta > 0.5 after a renormalization of the charge. The SU(2) and SU(3) Creutz
ratios robustly display quark confinement at beta = 0.5 and beta = 2,
respectively. At much weaker coupling, the SU(2) and SU(3) Creutz ratios agree
with perturbation theory after a renormalization of the coupling constant. For
SU(3) without quarks, our lattice QCD parameter is Lambda_L = 130 +- 18$ MeV.


title:
Application of the Coupled Cluster Method to a Hamiltonian Lattice Field
  Theory

abstract:
  The coupled cluster method has been applied to the eigenvalue problem lattice
Hamiltonian QCD (without quarks) for SU(2) gauge fields in two space
dimensions.
  Using a recently presented new formulation and the truncation prescription of
Guo et al. we were able to compute the ground state and the lowest
$0^+$-glueball mass up to the sixth order of the coupled cluster expansion.
  The results show evidence for a ``scaling window'' (i.e. good convergence and
constance of dimensionless quantities) around $\beta=4/g^2 \approx 3$.
  A comparison of our results to those of other methods is presented.


title: Strong Coupling Model for String Breaking on the Lattice

abstract:
  A model for SU(n) string breaking on the lattice is formulated using strong
coupling ideas. Although necessarily rather crude, the model gives an explicit
picture of string breaking in the presence of dynamical quarks as a mixing
phenomenon that involves the string state and a two-meson state. A careful
analysis, within the model, of the Wilson loop shows that the evolution of the
mixing angle as a function of separation may obscure the expected crossover
effect. If a sufficiently extensive mixing region exists then an appropriate
combination of transition amplitudes can help in revealing the effect.
  The sensitivity of the mixing region to the values of the meson energy and
the dynamical quark mass is explored and an assessment made of the
dectectibility of string breaking in a practical lattice simulation.


title: The universality class of the electroweak theory

abstract:
  We study the universality class and critical properties of the electroweak
theory at finite temperature. Such critical behaviour is found near the
endpoint m_H=m_{H,c} of the line of first order electroweak phase transitions
in a wide class of theories, including the Standard Model (SM) and a part of
the parameter space of the Minimal Sypersymmetric Standard Model (MSSM). We
find that the location of the endpoint corresponds to the Higgs mass m_{H,c} =
72(2) GeV in the SM with sin^2 theta_W = 0, and m_{H,c} < 80 GeV with sin^2
theta_W = 0.23. As experimentally m_H > 88 GeV, there is no electroweak phase
transition in the SM. We compute the corresponding critical indices and provide
strong evidence that the phase transitions near the endpoint fall into the
three dimensional Ising universality class.


title: Improved Lattice Actions with Chemical Potential

abstract:
  We give a prescription how to include a chemical potential \mu into a general
lattice action. This inclusion does not cause any lattice artifacts. Hence its
application to an improved - or even perfect - action at \mu =0 yields an
improved resp. perfect action at arbitrary \mu. For short-ranged improved
actions, a good scaling behavior holds over a wide region, and the upper bound
for the baryon density - which is known for the standard lattice actions - can
be exceeded.


title: Lattice QCD with Ginsparg-Wilson fermions

abstract:
  Lattice QCD using fermions whose Dirac operator obeys the Ginsparg-Wilson
relation, is perhaps the best known formulation of QCD with a finite cutoff. It
reproduces all the low energy QCD phenomenology associated with chiral symmetry
at finite lattice spacings. In particular it explains the origin of massless
pions due to spontaneous chiral symmetry breaking and leads to new ways to
approach the U(1) problem on the lattice. Here we show these results in the
path integral formulation and derive for the first time in lattice QCD a known
formal continuum relation between the chiral condensate and the topological
susceptibility. This relation leads to predictions for the critical behavior of
the topological susceptibility near the phase transition and can now be checked
in Monte-Carlo simulations even at finite lattice spacings.


title: Embedded Topological Defects in Hot Electroweak Theory: a Lattice Study

abstract:
  We study the properties of Nambu monopoles and Z-vortices in the 3D lattice
SU(2) Higgs theory which represents the Standard Model at high temperature. We
show that the densities of the Nambu monopoles and the Z-vortices are O(1) in
the symmetric phase and generically small in the Higgs phase. Near to the
critical Higgs mass and in the vicinity of the phase transition the densities
are no more negligible in the broken phase. The percolation probability of the
Z-vortex lines is found as a new disorder parameter for this phase transition.
We conclude that the transition to the symmetric phase is accompanied by
Z-vortex condensation. Simulations comparing elementary and extended vortices
and monopoles at different \beta_G values, aiming to show that the density of
vortices and monopoles of fixed physical size might have a well-defined
continuum limit, gives encouraging but so far inconclusive results.


title: The RANLUX generator: resonances in a random walk test

abstract:
  Using a recently proposed directed random walk test, we systematically
investigate the popular random number generator RANLUX developed by Luescher
and implemented by James. We confirm the good quality of this generator with
the recommended luxury level. At a smaller luxury level (for instance equal to
1) resonances are observed in the random walk test. We also find that the
lagged Fibonacci and Subtract-with-Carry recipes exhibit similar failures in
the random walk test. A revised analysis of the corresponding dynamical systems
leads to the observation of resonances in the eigenvalues of Jacobi matrix.


title: The Ginsparg-Wilson relation and local chiral random matrix theory

abstract:
  A chiral random matrix model with locality is constructed and examined. The
Nielsen-Ninomiya no-go theorem is circumvented by the use of a generally
applicable modified Dirac operator which respects the Ginsparg-Wilson relation.
We observe the expected universal behaviour of the eigenvalue density in the
microscopic limit.


title:
Two-dimensional Lattice Gross-Neveu Model with Wilson Fermion Action at
  Finite Temperature and Chemical Potential

abstract:
  We investigate the phase structure of the two-dimensional lattice Gross-Neveu
model formulated with the Wilson fermion action to leading order of 1/N
expansion. Structural change of the parity-broken phase under the influence of
finite temperature and chemical potential is studied. The connection between
the lattice phase structure and the chiral phase transition of the continuum
theory is clarified.


title: Equivariant Gauge Fixing of SU(2) Lattice Gauge Theory

abstract:
  I construct a Lattice Gauge Theory (LGT) with discrete Z_2 structure group
and an equivariant BRST symmetry that is physically equivalent to the standard
SU(2)-LGT. The measure of this Z_2-LGT is invariant under all the discrete
symmetries of the lattice and its partition function does not vanish. The
Topological Lattice Theories (TLT) that localize on the moduli spaces are
explicitly constructed and their BRST symmetry is exhibited. The ghosts of the
Z_2-invariant local LGT are integrated in favor of a nonlocal bosonic measure.
In addition to the SU(2) link variables and the coupling g^2, this effective
bosonic measure also depends on an auxiliary gauge invariant site variable of
canonical dimension two and on a gauge parameter \alpha. The relation between
the expectation value of the auxiliary field, the gauge parameter \alpha and
the lattice spacing $a$ is obtained to lowest order in the loop expansion. In
four dimensions and the critical limit this expectation value is a physical
scale proportional to \Lambda_L in the gauge \alpha=g^2 (11-n_f)/24+ O(g^4).
Implications for the loop expansion of observables in such a critical gauge are
discussed.


title:
Asymptotic expansion of the lattice scalar propagator in coordinate
  space

abstract:
  The asymptotic expansion of the massive scalar field propagator on a
n-dimensional lattice is derived. The method used is based on the evaluation of
the asymptotic expansion of the modified Bessel function $I_{\nu}(\nu^{2}
\beta)$ as the order $\nu$ grows to infinity.


title:
Finite Size Scaling and ``perfect'' actions: the three dimensional Ising
  model

abstract:
  Using Finite-Size Scaling techniques, we numerically show that the first
irrelevant operator of the lattice $\lambda\phi^4$ theory in three dimensions
is (within errors) completely decoupled at $\lambda=1.0$. This interesting
result also holds in the Thermodynamical Limit, where the renormalized coupling
constant shows an extraordinary reduction of the scaling-corrections when
compared with the Ising model. It is argued that Finite-Size Scaling analysis
can be a competitive method for finding improved actions.


title: Critical region of the finite temperature chiral transition

abstract:
  We study a Yukawa theory with spontaneous chiral symmetry breaking and with a
large number N of fermions near the finite temperature phase transition.
Critical properties in such a system can be described by the mean field theory
very close to the transition point. We show that the width of the region where
non-trivial critical behavior sets in is suppressed by a certain power of 1/N.
Our Monte Carlo simulations confirm these analytical results. We discuss
implications for the chiral phase transition in QCD.


title: Inverse Symmetry Breaking with 4d Lattice Simulations

abstract:
  According to resummed perturbation theory, certain scalar theories have a
global symmetry, which is restored in the vacuum but is broken at high
temperatures. Recently, this phenomenon has been studied with 4d finite
temperature lattice simulations, and it has been suggested that the
non-perturbative dynamics thus incorporated would hinder the transition. We
have carried out another lattice study, for a theory with very small coupling
constants. We find perfect compatibility with next-to-leading order resummed
perturbation theory, and demonstrate that ``inverse'' symmetry breaking can
indeed take place at high temperatures.


title:
Renormalized couplings and scaling correction amplitudes in the N-vector
  spin models on the sc and the bcc lattices

abstract:
  For the classical N-vector model, with arbitrary N, we have computed through
order \beta^{17} the high temperature expansions of the second field derivative
of the susceptibility \chi_4(N,\beta) on the simple cubic and on the body
centered cubic lattices. (The N-vector model is also known as the O(N)
symmetric classical spin Heisenberg model or, in quantum field theory, as the
lattice
  O(N) nonlinear sigma model.) By analyzing the expansion of \chi_4(N,\beta) on
the two lattices, and by carefully allowing for the corrections to scaling, we
obtain updated estimates of the critical parameters and more accurate tests of
the hyperscaling relation d\nu(N) +\gamma(N) -2\Delta_4(N)=0 for a range of
values of the spin dimensionality N, including
  N=0 [the self-avoiding walk model], N=1 [the Ising spin 1/2 model],
  N=2 [the XY model], N=3 [the classical Heisenberg model]. Using the recently
extended series for the susceptibility and for the second correlation moment,
we also compute the dimensionless renormalized four point coupling constants
and some universal ratios of scaling correction amplitudes in fair agreement
with recent renormalization group estimates.


title: Ordering monomial factors of polynomials in the product representation

abstract:
  The numerical construction of polynomials in the product representation (as
used for instance in variants of the multiboson technique) can become
problematic if rounding errors induce an imprecise or even unstable evaluation
of the polynomial. We give criteria to quantify the effects of these rounding
errors on the computation of polynomials approximating the function $1/s$. We
consider polynomials both in a real variable $s$ and in a Hermitian matrix. By
investigating several ordering schemes for the monomials of these polynomials,
we finally demonstrate that there exist orderings of the monomials that keep
rounding errors at a tolerable level.


title: Witten's SU(2) anomaly on the lattice

abstract:
  Witten's anomaly for SU(2) with a single I=1/2 Weyl fermion in four dimension
is shown to be reproduced by the lattice overlap. The mechanism is based on
Berry's phase, and on the analyticity of the matrix $H$ by which the overlap is
defined.


title: A Lattice Study of Spectator Effects in Inclusive Decays of B-Mesons

abstract:
  We compute the matrix elements of the operators which contribute to spectator
effects in inclusive decays of $B$-mesons. The results agree well with
estimates based on the vacuum saturation (factorization) hypothesis. For the
ratio of lifetimes of charged and neutral mesons we find
$\tau(B^-)/\tau(B_d)=1.03\pm 0.02\pm 0.03$, where the first error represents
the uncertainty in our evaluation of the matrix elements, and the second is an
estimate of the uncertainty due to the fact that the Wilson coefficient
functions have only been evaluated at tree-level in perturbation theory. This
result is in agreement with the experimental measurement. We also discuss the
implications of our results for the semileptonic branching ratio and the charm
yield.


title: Scalar Quarkonium Masses and Mixing with the Lightest Scalar Glueball

abstract:
  We evaluate the continuum limit of the valence (quenched) approximation to
the mass of the lightest scalar quarkonium state, for a range of different
quark masses, and to the mixing energy between these states and the lightest
scalar glueball. Our results support the interpretation of $f_0(1710)$ as
composed mainly of the lightest scalar glueball.


title: Fractional Inversion in Krylov Space

abstract:
  The fractional inverse $M^{-\gamma}$ (real $\gamma >0$) of a matrix $M$ is
expanded in a series of Gegenbauer polynomials. If the spectrum of $M$ is
confined to an ellipse not including the origin, convergence is exponential,
with the same rate as for Chebyshev inversion. The approximants can be improved
recursively and lead to an iterative solver for $M^\gamma x = b$ in Krylov
space. In case of $\gamma = 1/2$, the expansion is in terms of Legendre
polynomials, and rigorous bounds for the truncation error are derived.


title:
A Possible Lack of Phase Transition in SO(3) Lattice Gauge Theory on
  Lattices with Two Temporal Sites

abstract:
  This paper is being withdrawn as its main results are already included in
section 2 of the paper hep-lat/9901006.


title: On Lattice Computations of K+ --> pi+ pi0 Decay at m_K =2m_pi

abstract:
  We use one-loop chiral perturbation theory to compare potential lattice
computations of the K+ --> pi+ pi0 decay amplitude at m_K=2m_pi with the
experimental value. We find that the combined one-loop effect due to this
unphysical pion to kaon mass ratio and typical finite volume effects is still
of order minus 20-30%, and appears to dominate the effects from quenching.


title:
Thermodynamics of Lattice QCD with 2 Quark Flavours: Chiral Symmetry and
  Topology

abstract:
  We have studied the restoration of chiral symmetry in lattice QCD at the
finite temperature transition from hadronic matter to a quark-gluon plasma. By
measuring the screening masses of flavour singlet and non-singlet meson
excitations, we have seen evidence that, although flavour chiral symmetry is
restored at this transition, flavour singlet (U(1)) axial symmetry is not. We
conclude that this indicates that instantons continue to play an important role
in the quark-gluon plasma phase.


title: Quenched Chiral Artifacts for Wilson-Dirac Fermions

abstract:
  We examine artifacts associated with the chiral symmetry breaking induced
through the use of Wilson-Dirac fermions in lattice Monte Carlo computations.
For light quark masses, the conventional quenched theory can not be defined
using direct Monte Carlo methods due to the existence of nonintegrable poles in
physical quantities. These poles are associated with the real eigenvalue
spectrum of the Wilson-Dirac operator. We show how this singularity structure
can be observed in the analysis of both QED in two dimensions and QCD in four
dimensions.


title:
Statistical analysis and the equivalent of a Thouless energy in lattice
  QCD Dirac spectra

abstract:
  Random Matrix Theory (RMT) is a powerful statistical tool to model spectral
fluctuations. This approach has also found fruitful application in Quantum
Chromodynamics (QCD). Importantly, RMT provides very efficient means to
separate different scales in the spectral fluctuations. We try to identify the
equivalent of a Thouless energy in complete spectra of the QCD Dirac operator
for staggered fermions from SU(2) lattice gauge theory for different lattice
size and gauge couplings. In disordered systems, the Thouless energy sets the
universal scale for which RMT applies. This relates to recent theoretical
studies which suggest a strong analogy between QCD and disordered systems. The
wealth of data allows us to analyze several statistical measures in the bulk of
the spectrum with high quality. We find deviations which allows us to give an
estimate for this universal scale. Other deviations than these are seen whose
possible origin is discussed. Moreover, we work out higher order correlators as
well, in particular three--point correlation functions.


title: Thermodynamics of One-flavour QCD

abstract:
  We give a brief introduction on finite temperature phase transitions in
lattice QCD including a discussion on the identification of first order
transitions. We present a study of the deconfinement phase transition of
one-flavour QCD, using the multiboson algorithm on lattice of sizes $8^3$,
$12^3$ and $16^3\times 4$. For heavy quarks our results are characteristic of a
first order phase transition which gets weaker as the quark mass decreases and
ends at a critical value of $\kappa \sim 0.1$ or in physical units at about 1.6
GeV.


title:
Precision computation of a low-energy reference scale in quenched
  lattice QCD

abstract:
  We present results for the reference scale r_0 in SU(3) Lattice Gauge Theory
for beta = 6/g_0^2 in the range 5.7 <= beta <= 6.57. The high relative accuracy
of 0.3-0.6% in r_0/a was achieved through good statistics, the application of a
multi-hit procedure and a variational approach in the computation of Wilson
loops. A precise definition of the force used to extract r_0 has been used
throughout the calculation which guarantees that r_0/a is a smooth function of
the bare coupling and that subsequent continuum extrapolations are possible.
The results are applied to the continuum extrapolations of the energy gap Delta
in the static quark potential and the scale L_max/r_0 used in the calculation
of the running coupling constant.


title: Non-perturbative Renormalization of Quark bilinears

abstract:
  We compute non-perturbatively the renormalization constants of quark
bilinears on the lattice in the quenched approximation at three values of the
coupling beta=6/g_0^2=6.0,6.2,6.4 using both the Wilson and the tree-level
improved SW-Clover fermion action. We perform a Renormalization Group analysis
at the next-to-next-to-leading order and compute Renormalization Group
invariant values for the constants. The results are applied to obtain a fully
non-perturbative estimate of the vector and pseudoscalar decay constants.


title:
Non-perturbative determination of anisotropy coefficients in lattice
  gauge theories

abstract:
  We propose a new non-perturbative method to compute derivatives of gauge
coupling constants with respect to anisotropic lattice spacings (anisotropy
coefficients), which are required in an evaluation of thermodynamic quantities
from numerical simulations on the lattice. Our method is based on a precise
measurement of the finite temperature deconfining transition curve in the
lattice coupling parameter space extended to anisotropic lattices by applying
the spectral density method. We test the method for the cases of SU(2) and
SU(3) gauge theories at the deconfining transition point on lattices with the
lattice size in the time direction $N_t=4$ -- 6. In both cases, there is a
clear discrepancy between our results and perturbative values. A longstanding
problem, when one uses the perturbative anisotropy coefficients, is a
non-vanishing pressure gap at the deconfining transition point in the SU(3)
gauge theory. Using our non-perturbative anisotropy coefficients, we find that
this problem is completely resolved: we obtain $\Delta p/T^4 = 0.001(15)$ and
$-0.003(17)$ on $N_t=4$ and 6 lattices, respectively.