title:
QCD chiral Lagrangian on the lattice, strong coupling expansion and Ward
  identities with Wilson fermions

abstract:
  We discuss a general strategy to compute the coefficients of the QCD chiral
Lagrangian using lattice QCD with Wilson fermions. This procedure requires the
introduction of a lattice chiral Lagrangian as an intermediate step in the
calculation. The QCD chiral Lagrangian is then obtained by expanding the
lattice effective theory in increasing powers of the lattice spacing and the
external momenta. In order to investigate the consequences of the chiral
symmetry breaking induced by the Wilson term, we study the lattice chiral
Lagrangian at the leading order of the strong coupling and large $N$ expansion.
We show that the effects of the Wilson term can be conveniently taken into
account, in the lattice effective theory, by a suitable renormalization
procedure. In particular, we show that, at the leading order of the strong
coupling and large N expansion, the chiral symmetry is exactly recovered on the
lattice provided that the bare quark mass and the lattice operators are
properly renormalized.


title: Dimensionally reduced U(1)+Higgs theory in the broken phase

abstract:
  We apply dimensional reduction to the finite temperature U(1)+Higgs theory
and study the properties of the reduced 3-dimensional theory in the broken
phase using lattice Monte Carlo simulations. We compute analytically the scalar
condensate in optimized 2-loop perturbation theory and the correlators in
1-loop perturbation theory. These quantities are also calculated numerically.
The two results for the condensate agree well but a 25\% difference is observed
for the scalar correlator, indicating the need for optimized 2-loop
perturbative results.


title: Charged Pion Polarizability from the Lattice

abstract:
  Direct evaluation of charged particle polarizabilities on the lattice is
quite difficult. However, a short cut for charged pion polarizability - the
Das, Mathur, Okubo Sum Rule - can readily be calculated using lattice
techniques. A phenomenological model has been developed to fit the time
behavior of the propagators in this expression. Numerical systematics are
discussed and some preliminary results are presented.


title:
Towards a lattice calculation of the coefficients of the QCD chiral
  Lagrangian

abstract:
  We discuss a general strategy to compute the coefficients of QCD chiral
Lagrangian by using the lattice regularization of QCD with Wilson fermions.
This procedure requires the introduction of an effective Lagrangian for lattice
QCD as an intermediate step in the calculation. The continuum QCD chiral
Lagrangian can be then obtained by expanding the lattice effective Lagrangian
in increasing powers of the external momenta. A suitable renormalization
procedure is required to account for the chiral symmetry breaking introduced by
the Wilson term in the lattice action. In anticipation of a numerical
simulation, the lattice effective Lagrangian is computed analytically and
investigated in the strong coupling and large $N$ limit


title:
Matching numerical simulations to continuum field theories: A lattice
  renormalization study

abstract:
  The study of nonlinear phenomena in systems with many degrees of freedom
often relies on complex numerical simulations. In trying to model realistic
situations, these systems may be coupled to an external environment which
drives their dynamics. For nonlinear field theories coupled to thermal (or
quantum) baths, discrete lattice formulations must be dealt with extreme care
if the results of the simulations are to be interpreted in the continuum limit.
Using techniques from renormalization theory, a self-consistent method is
presented to match lattice results to continuum models. As an application,
symmetry restoration in $\phi^4$ models is investigated.


title: The Taming of QCD by Fortran 90

abstract:
  We implement lattice QCD using the Fortran 90 language. We have designed
machine independent modules that define fields (gauge, fermions, scalars,
etc...) and have defined overloaded operators for all possible operations
between fields, matrices and numbers. With these modules it is very simple to
write QCD programs. We have also created a useful compression standard for
storing the lattice configurations, a parallel implementation of the random
generators, an assignment that does not require temporaries, and a machine
independent precision definition. We have tested our program on parallel and
single processor supercomputers obtaining excellent performances.


title:
Exploring the Unstable Modes Dynamics by the Lattice Schrodinger
  Functional

abstract:
  We analyze the problem of the Nielsen-Olesen unstable modes in the $SU(2)$
lattice gauge theory by means of a recently introduced gauge-invariant
effective action. We perform numerical simulations in the case of a constant
Abelian chromomagnetic field. We find that for lattice sizes above a certain
critical length the density of effective action shows a behaviour compatible
with the presence of the unstable modes.


title: The Spectrum of the 2+1 Dimensional Gauge Ising Model

abstract:
  We present a high precision Monte Carlo study of the spectrum of the $Z_2$
gauge theory in $2+1$ dimensions in the strong coupling phase. Using state of
the art Monte Carlo techniques we are able to accurately determine up to three
masses in a single channel. We compare our results with the strong coupling
expansion for the lightest mass and with results for the universal ratio
$\sigma/m^2$ determined for the $\phi^4$-theory. Finally the whole spectrum is
compared with that obtained from the Isgur-Paton flux tube model and the
spectrum of the $2+1$ dimensional $SU(2)$ gauge theory. A remarkable agreement
between the Ising and SU(2) spectra (except for the lowest mass state) is
found.


title:
Logarithmic Corrections and Finite-Size Scaling in the Two-Dimensional
  4-State Potts Model

abstract:
  We analyze the scaling and finite-size-scaling behavior of the
two-dimensional 4-state Potts model. We find new multiplicative logarithmic
corrections for the susceptibility, in addition to the already known ones for
the specific heat. We also find additive logarithmic corrections to scaling,
some of which are universal. We have checked the theoretical predictions at
criticality and off criticality by means of high-precision Monte Carlo data.


title: Exotic hybrid mesons with light quarks

abstract:
  Hybrid mesons, made from a quark, an antiquark and gluons, can have quantum
numbers inaccessible to conventional quark-antiquark states. Confirmation of
such states would give information on the role of "dynamical" color in low
energy QCD. We present preliminary results for hybrid meson masses using light
Wilson valence quarks.


title: Electromagnetic Structure of Light Baryons in Lattice QCD

abstract:
  A method for computing electromagnetic properties of hadrons in lattice QCD
is applied to the extraction of electromagnetic properties of the octet
baryons. This allows a determination of the full dependence of the baryon
masses on the charges and masses of the valence quarks. Results of a first
numerical study (at $\beta=5.7$ with Wilson action and light quark masses fixed
from the pseudoscalar meson spectrum) are reported. The octet baryon
isomultiplet splittings (with statistical errors) are found to be: ${\rm N} -
{\rm P} = 1.55(\pm 0.56)$, $\Sigma^0 - \Sigma^+ = 2.47(\pm 0.39)$, $\Sigma^- -
\Sigma^0 = 4.63(\pm 0.36)$ and $\Xi^- - \Xi^0 = 5.68(\pm 0.24)$ MeV. Estimates
of the systematic corrections arising from finite volume and the quenched
approximation are included in these results.


title:
Softening of First-Order Phase Transition on Quenched Random Gravity
  Graphs

abstract:
  We perform extensive Monte Carlo simulations of the 10-state Potts model on
quenched two-dimensional $\Phi^3$ gravity graphs to study the effect of
quenched coordination number randomness on the nature of the phase transition,
which is strongly first order on regular lattices. The numerical data provides
strong evidence that, due to the quenched randomness, the discontinuous
first-order phase transition of the pure model is softened to a continuous
transition, representing presumably a new universality class. This result is in
striking contrast to a recent Monte Carlo study of the 8-state Potts model on
two-dimensional Poissonian random lattices of Voronoi/Delaunay type, where the
phase transition clearly stayed of first order, but is in qualitative agreement
with results for quenched bond randomness on regular lattices. A precedent for
such softening with connectivity disorder is known: in the 10-state Potts model
on annealed Phi3 gravity graphs a continuous transition is also observed.


title: Quantum fluctuations of the color flux tube

abstract:
  The quantum fluctuations of the flux tube joining two static sources in the
confining phase of a lattice gauge theory are described by an effective string
theory. The predictions of the latter for ratios of Wilson loops of equal
perimeter do not contain any free parameters, and can be computed exactly for
large Wilson loops. We compare these predictions with numerical results in 3D
$Z_2$ gauge theory, finding complete agreement.


title: Supersymmetric gauge theories on the lattice

abstract:
  The perspectives of numerical simulations in supersymmetric quantum field
theories with vector-like gauge symmetries are discussed. A numerical
simulation algorithm for SU(2) gauge theory with gluinos is studied and the
first results on the glueball-gluinoball spectrum are presented.


title:
Scaling behavior at the tricritical point in the fermion-gauge-scalar
  model

abstract:
  We investigate a strongly coupled U(1) gauge theory with fermions and scalars
on the lattice and analyze whether the continuum limit might be a
renormalizable theory with dynamical mass generation. Most attention is paid to
the phase with broken chiral symmetry in the vicinity of the tricritical point
found in the model. There we investigate the scaling of the masses of the
composite fermion and of some bosonic bound states. As a by-product we confirm
the mean-field exponents at the endpoint in the U(1)-Higgs model, by analyzing
the scaling of the Fisher zeros.


title:
Non-Gaussian fixed point candidates in the 4D compact U(1) gauge
  theories

abstract:
  Some interesting nonperturbative properties of the strongly coupled 4D
compact U(1) lattice gauge theories, both without and with matter fields, are
pointed out. We demonstrate that the pure gauge theory has a non-Gaussian fixed
point with $\nu = 0.365(8)$ at the second order confinement-Coulomb phase
transition. Thus a non-asymptotic free and nontrivial continuum limit of this
theory, and of its various dual equivalents, in particular of a special case of
the effective string theory, can be constructed. Including a scalar matter
field (compact scalar QED), we confirm the Gaussian behavior at the endpoint of
the Higgs phase transition line. In the theory with both scalar and fermion
matter fields, we demonstrate the existence of a tricritical point. Here, the
chiral symmetry is broken, and the mass of unconfined composite fermions is
generated dynamically. Appart from the Goldstone bosons, the spectrum contains
also a massive scalar. This resembles the Higgs-Yukawa sector of the SM, albeit
of dynamical origin, like the Nambu--Jona-Lasinio model. However, the scaling
behavior is different from that in the NJL model and the nonperturbative
renormalizability might thus be possible.


title: U(1) Gauge Theory with Villain Action on Spherical Lattices

abstract:
  We have studied the U(1) gauge field theory with Villain (periodic Gaussian)
action on spherelike lattices. The effective size of the systems studied ranges
from 6 to 16. We do not observe any 2-state signal in the distribution function
of the plaquette expectation value at the deconfining phase transition. The
observed finite-size scaling behavior is consistent with a second order phase
transition. The obtained value of the critical exponent is nu =0.366(12) and
thus neither Gaussian (nu = 0.5) nor discontinuous (nu=0.25) type, indicating a
nontrivial continuum limit.


title: Numerical simulation of random paths with a curvature dependent action

abstract:
  We study an ensemble of closed random paths, embedded in R^3, with a
curvature dependent action. Previous analytical results indicate that there is
no crumpling transition for any finite value of the curvature coupling.
Nevertheless, in a high statistics numerical simulation, we observe two
different regimes for the specific heat separated by a rather smooth structure.
The analysis of this fact warns us about the difficulties in the interpretation
of numerical results obtained in cases where theoretical results are absent and
a high statistics simulation is unreachable. This may be the case of random
surfaces.


title: Random paths with curvature

abstract:
  We present some results coming from a Monte Carlo simulation of a set of
random paths with a curvature dependent action. This model can be considered as
a toy model of the theory of random surfaces. The transition from free to rigid
random paths has been analyzed and the similitude with the crumpling transition
have been pointed out.


title: Finite size analysis of the pseudo specific heat in SU(2) gauge theory

abstract:
  We investigate the pseudo specific heat of SU(2) gauge theory near the
crossover point on $4^4$ to $16^4$ lattices. Several different methods are used
to determine the specific heat. The curious finite size dependence of the peak
maximum is explained from the interplay of the crossover phenomenon with the
deconfinement transition occurring due to the finite extension of the lattice.
In this context we calculate the modulus of the lattice average of the Polyakov
loop on symmetric lattices and compare it to the prediction from a random walk
model.


title: Universal correlations in spectra of the lattice QCD Dirac operator

abstract:
  Recently, Kalkreuter obtained complete Dirac spectra for $SU(2)$ lattice
gauge theory both for staggered fermions and for Wilson fermions. The lattice
size was as large as $12^4$. We performed a statistical analysis of these data
and found that the eigenvalue correlations can be described by the Gaussian
Symplectic Ensemble for staggered fermions and by the Gaussian Orthogonal
Ensemble for Wilson fermions. In both cases long range spectral fluctuations
are strongly suppressed: the variance of a sequence of levels containing $n$
eigenvalues on average is given by $\Sigma_2(n) \sim 2 (\log n)/\beta\pi^2 $
($\beta$ is equal to 4 and 1, respectively) instead of $\Sigma_2(n) = n$ for a
random sequence of levels. Our findings are in agreement with the anti-unitary
symmetry of the lattice Dirac operator for $N_c=2$ with staggered fermions
which differs from Wilson fermions (with the continuum anti-unitary symmetry).
For $N_c = 3$, we predict that the eigenvalue correlations are given by the
Gaussian Unitary Ensemble.


title: QCD with dynamical Wilson fermions at $\beta=5.5$

abstract:
  We study QCD with two flavors of dynamical Wilson fermions at $\beta = 5.5$
and three values of $\kappa$. The corresponding pion masses are 0.375, 0.324
and 0.262 in lattice units, with pion to rho mass ratios of 0.76, 0.71 and
0.62, respectively. We use the configurations to compute the heavy quark
potential, leading to lattice spacings of 0.110, 0.105 and 0.099 fm, and to
compute spectroscopy for several different valence quark $\kappa$'s.


title: Representation of Complex Probabilities

abstract:
  Let a ``complex probability'' be a normalizable complex distribution $P(x)$
defined on $\R^D$. A real and positive probability distribution $p(z)$, defined
on the complex plane $\C^D$, is said to be a positive representation of $P(x)$
if $\langle Q(x)\rangle_P = \langle Q(z)\rangle_p$, where $Q(x)$ is any
polynomial in $\R^D$ and $Q(z)$ its analytical extension on $\C^D$. In this
paper it is shown that every complex probability admits a real representation
and a constructive method is given. Among other results, explicit positive
representations, in any number of dimensions, are given for any complex
distribution of the form Gaussian times polynomial, for any complex
distributions with support at one point and for any periodic Gaussian times
polynomial.


title:
Analytical and Numerical Study of the Aharonov--Bohm Effect in 3D and 4D
  Abelian Higgs Model

abstract:
  We discuss the Aharonov--Bohm effect in three and four dimensional
non--compact lattice Abelian Higgs model. We show analytically that this effect
leads to the long--range Coulomb interaction of the charged particles, which is
confining in three dimensions. The Aharonov--Bohm effect is found in numerical
calculations in 3D Abelian Higgs model.


title: Two Flavour QCD Phase Transition

abstract:
  Results on the phase transition in QCD with two flavours of light staggered
fermions from an ongoing simulation are presented. We find the restoration of
the chiral SU(2) x SU(2) symmetry, but not of the axial U_A(1) symmetry.


title: Undoubled Chiral Fermions on a Lattice

abstract:
  We analyze the dynamics of an $SU_L(2)\otimes U_R(1)$ chiral theory on the
lattice with a strong multifermion coupling. It is shown that no spontaneous
symmetry breaking occurs; the ``spectator'' fermion $\psi_R$ is a free mode;
doublers are decoupled as massive Dirac fermions consistently with the chiral
symmetries. In 1+1 dimension, we show that the right-handed three-fermion state
disappears at the threshold and an undoubled left-handed chiral fermion remains
in the continuum limit.


title: Scaling in the two-dimensional U(1)--Higgs model

abstract:
  We study the continuum limit of the $2D$ U(1)--Higgs model with variable
scalar field length, which is qualitatively different from the fixed length
case. Our simulations concentrate on the scaling behaviour of the topological
susceptibility, and an instanton-induced confinement mechanism of fractional
charges is numerically confirmed.


title: Hybrid Monte Carlo and topological modes of full QCD

abstract:
  We investigate the performance of the hybrid Monte Carlo algorithm, the
standard algorithm used for lattice QCD simulations involving fermions, in
updating non-trivial global topological structures. We find that the hybrid
Monte Carlo algorithm has serious problems decorrelating the global topological
charge at the values of $\beta$ and $m$ currently simulated, where continuum
physics should be approximately realized. This represents a warning which must
be seriously considered when simulating full QCD by hybrid Monte Carlo.


title: Worldsheet Formulation for Lattice Staggered Fermions

abstract:
  The worldsheet formulation is introduced for lattice gauge theories with
dynamical fermions. The partition function of lattice compact QED with
staggered fermions is expressed as a sum over surfaces with border on
self-avoiding fermionic paths. The surfaces correspond to the world sheets of
loop-like pure electric flux excitations and meson-like configurations (open
electric flux tubes carrying matter fields at their ends). The proposed
formulation does not have the problem of the additional doubling of the fermion
species due to the discretization of time. The gauge non-redundancy and the
geometric transparency are two appealing features of this description. From the
computational point of view, the partition function involves fewer degrees of
freedom than the Kogut-Susskind formulation and offers an alternative and more
economic framework to perform numerical computations with dynamical fermions.


title: Recent Developments in Fermion Simulation Algorithms

abstract:
  A summary of recent developments in the field of simulation algorithms for
dynamical fermions is given.


title: Topological transitions in the euclidean 2d U(1)-Higgs model

abstract:
  The two-dimensional U(1)-gauged Higgs model is studied on an euclidean
lattice of size $L_1\times L_2$, where the temperature $T=L_2^{-1}$ is of the
order of the sphaleron mass. The simulation parameters are taken from zero
temperature results. By comparison with classical and semiclassical results I
discuss, whether the sphaleron transition rate can be extracted from the
behavior of the Chern-Simons number and from the formation of vortices in an
euclidean simulation at high temperatures.


title: Some Cautionary Remarks on Abelian Projection and Abelian Dominance

abstract:
  Some critical remarks are presented, concerning the abelian projection theory
of quark confinement.


title: Three topics of monopole dynamics in abelian projected QCD

abstract:
  Three topics about monopole dynamics after abelian projection are reported.
The first is the new and detailed analyses of $SU(2)$ monopole action obtained
after the block-spin transformation on the dual lattice. The $b=na(\beta)$
dependence for all couplings are well fitted with a universal curve. The
distance dependence of the couplings is well reproduced by a massive propagator
with the mass $m=0.8$ in unit of $b$. The second is the $SU(3)$ monopole action
recently obtained. The third is new interesting gauges showing abelian and
monopole dominances as in the maximally abelian gauge.


title:
A High-Statistics Lattice Calculation of $\lambda_1$ and $\lambda_2$ in
  the $B$ meson

abstract:
  We present a high-statistics lattice calculation of the kinetic energy
$-\lambda_1/2 m_b$ of the heavy quark inside the $B$-meson and of the
chromo-magnetic term $\lambda_2$, related to the $B^*$--$B$ mass splitting,
performed in the HQET. Our results have been obtained from a numerical
simulation based on 600 gauge field configurations generated at $\beta=6.0$, on
a lattice volume $24^3 \times 40$ and using, for the meson correlators, the
results obtained with the SW-Clover $O(a)$ improved lattice action for the
light quarks. For the kinetic energy we found $-\lambda_1=\langle B \vert \bar
h (i\vec{D})^{2} h \vert B \rangle /(2 M_B )=-(0.09 \pm 0.14)$~GeV$^2$, which
is interesting for phenomenological applications. We also find $\lambda_2= 0.07
\pm 0.01$ GeV$^2$, corresponding to $M^2_{B^*}-M^2_B= 4 \lambda_2= 0.280 \pm
0.060 $ GeV$^2$, which is about one half of the experimental value. The origin
of the discrepancy with the experimental number needs to be clarified.


title: Studies on the Chiral Order Parameter in the Schwinger Model

abstract:
  Based on an analytical technique using a unitary transformation and the
variational method, we study the chiral order parameter in the Schwinger model
in the lattice formalism with Kogut-Susskind fermions. The fermion condensate
$\langle {\bar\Psi} \Psi \rangle $ for any coupling constant and fermion mass
are calculated. Chiral symmetry is shown to be broken in the massless limit and
good scaling behavior is obtained.


title:
Study of Liapunov Exponents and the Reversibility of Molecular Dynamics
  Algorithms

abstract:
  We study the question of lack of reversibility and the chaotic nature of the
equations of motion in numerical simulations of lattice QCD.


title: Light hadron masses with an $O(a^2)$ improved NNN action

abstract:
  Meson and baryon masses in the light (u,d and s) sector are calculated using
tadpole-improved gauge field and fermion actions. These are corrected to order
$O(a^2)$ on the classical level using next-nearest-neighbour terms. The
results, obtained at lattice spacings of 0.4 and 0.27fm, are compared to Wilson
action calculations.


title: The rho meson decay constant using a tadpole-improved action

abstract:
  The rho meson decay constant and the associated renormalization factor are
computed in the quenched approximation on coarse lattices using a
tadpole-improved action which is corrected at the classical level to O(a^2).
The improvement is displayed by comparing to Wilson action calculations.


title:
Dirac operator as a random matrix and the quenched limit of QCD with
  chemical potential

abstract:
  The behavior of quenched QCD at nonzero chemical potential $\mu$ has been a
long-standing puzzle. An explicit solution is found using the random matrix
approach to chiral symmetry breaking. At nonzero $\mu$ the quenched QCD is not
a simple $n\to0$ limit of a theory with $n$ quarks: a naive `replica trick'
fails. A limit that leads to the quenched QCD is that of a theory with $2n$
quarks: $n$ quarks with original action and $n$ quarks with conjugate action.


title:
Classical improvement of lattice actions and quantum effects: a unified
  view

abstract:
  The possibility of removing the one-loop perturbative effects of lattice
artifacts by a proper choice of the lattice action is explored, and found to
depend crucially on the properties of the physical quantity considered. In this
respect the finite-space-volume mass gap m(L) is an improved observable. We
find an explicit momentum space representation of the one-loop contribution to
m(L) for arbitrary lattice actions in the case of two-dimensional O(N) sigma
models. We define a ``tree perfect'' Symanzik action and find that it formally
removes all one-loop lattice artifacts in m(L). On-shell improved actions do
not share this property.


title:
Detailed Phase Transition Study at M_H <= 70 GeV in a 3-dimensional
  $SU(2)$--Higgs Model

abstract:
  We study the electroweak phase transition in an effective 3-dimensional
theory for a Higgs mass of about 70 GeV by Monte Carlo simulations. The
transition temperature and jumps of order parameters are obtained and
extrapolated to the continuum using multi-histogram techniques and finite size
analysis.


title:
Physics of the Electroweak Phase Transition at M_H <= 70 GeV in a
  3-dimensional SU(2)-Higgs Model

abstract:
  Physical parameters of the electroweak phase transition in a 3d effective
lattice SU(2)-Higgs model are presented. The phase transition temperatures,
latent heats and continuum condensate discontinuities are measured at Higgs
masses of about 70 and 35 GeV. Masses and Higgs condensates are compared to
perturbation theory in the broken phase. In the symmetric phase bound states
and the static force are determined.


title:
Polyakov Loops and Magnetic Screening from Monopoles in SU(2) Lattice
  Gauge Theory

abstract:
  We present results from magnetic monopoles in $SU(2)$ lattice gauge theory at
finite temperature. The lattices are $16^{3}\times N_{t}$, for
$N_{t}=4,6,8,12$, at $\beta=2.5115$. Quantities discussed are: the spacial
string tension, Polyakov loops, and the screening of timelike and spacelike
magnetic currents.


title: Topological susceptibility through the deconfining phase transition

abstract:
  We present a measurement of the topological susceptibility in SU(3)
Yang-Mills theory through the deconfinement phase transition. An improved
operator is used for the topological charge density. A drop by an order of
magnitude is observed from the confined to the deconfined phase.


title:
Critical behavior of the correlation function of three-dimensional O(N)
  models in the symmetric phase

abstract:
  We present new strong-coupling series for O(N) spin models in three
dimensions, on the cubic and diamond lattices. We analyze these series to
investigate the two-point Green's function G(x) in the critical region of the
symmetric phase. This analysis shows that the low-momentum behavior of G(x) is
essentially Gaussian for all N from zero to infinity. This result is also
supported by a large-N analysis.


title: QCD at finite temperature and partially negative flavour numbers

abstract:
  We study dynamical fermion effects in lattice QCD at finite temperature. The
method adopted is basically the extrapolation from negative flavour numbers
already tested at zero temperature and based on the simulation of local bosonic
theories, with an essential difference. With an appropriate choice of the
boundary conditions on the bosonic fields, called ``bermions'', it is possible
to separate the $Z_3$ breaking contribution of fermion loops to the effective
action from the one conserving $Z_3$: the former is simulated exactly at a
fixed positive and even flavour number, while the extrapolation from negative
flavour numbers is made only on the $Z_3$ invariant part of the action. We test
this approach by comparing our results on a $16^3\times 2$ lattice with those
from a hopping parameter expansion and our results on a $16^3\times 4$ lattice
with those of direct Monte Carlo simulations including the fermion determinant.


title: SO(3) monopoles, vortices and confinement in SU(2) gauge theory

abstract:
  We report on further progress in our programme of understanding confinement
in 3d and 4d SU(2) gauge theory in terms of Z(2) monopoles. A sufficient
condition for confinement was previously translated into Z(2) monopole
correlation inequalities in a related SO(3) gauge theory. We shall discuss the
physical picture underlying this scenario and present some Monte Carlo evidence
concerning the monopole correlation inequalities.


title: Classical solutions in lattice gauge theories

abstract:
  The solutions of the classical equations of motion on a periodic lattice are
found which correspond to abelian single and double Dirac sheets. These
solutions exist also in non--abelian theories. Possible applications of these
solutions to the calculation of gauge dependent and gauge invariant observables
are discussed.


title: Strongly Coupled QED

abstract:
  A short review of some of the most relevant contributions to non-perturbative
QED is done. Since a Gaussian behaviour of QED \`a la $\lambda\phi^4$ has been
ruled out by the numerical data, I analyse the other two most reliable
scenarios, i.e. triviality \`a la Nambu-Jona Lasinio and non-Gaussian critical
behaviour. I give a suggestive theoretical argument against a Gaussian
behaviour of QED \`a la Nambu-Jona Lasinio, and show how the numerical data for
the susceptibility at the critical point of QED support this result.


title:
Complex Probability Distributions: A Solution for the Long-Standing
  Problem of QCD at Finite Density

abstract:
  We show how the prescription of taking the absolute value of the fermion
determinant in the integration measure of QCD at finite density, forgetting its
phase, reproduces the correct thermodynamical limit. This prescription, which
applies also to other gauge theories with non-positive-definite integration
measure, also has the advantage of killing finite size effects due to extremely
small mean values of the cosine of the phase of the fermion determinant. We
also give an explanation for the pathological behaviour of quenched QCD at
finite density.


title: A first study of the semi-leptonic decay of the $\Lambda_b$ baryon

abstract:
  We present the preliminary results of the first Lattice study of the baryonic
Isgur and Wise function obtained from the matrix element of the weak current
between $\Lambda$-baryon external states. Its dependence on the heavy and light
quark masses is studied. Some result on the semi-leptonic decay
$\Lambda_b\to\Lambda_c +l\nu$ are given.


title: Functional integration on Regge geometries

abstract:
  We adopt the standard definition of diffeomorphism for Regge gravity in D=2
and give an exact expression of the Liouville action in the discretized case.
We also give the exact form of the integration measure for the conformal
factor. In D>2 we extend the approach to any family of geometries described by
a finite number of parameters. The ensuing measure is a geometric invariant and
it is also invariant in form under an arbitrary change of parameters.


title:
A Renormalization Group for Dynamical Triangulations in Arbitrary
  Dimensions

abstract:
  A block spin renormalization group approach is proposed for the dynamical
triangulation formulation of quantum gravity in arbitrary dimensions.
Renormalization group flow diagrams are presented for the three-dimensional and
four-dimensional theories near their respective transitions.


title: Dual vortices in Abelian projected SU(2) in the Polyakov gauge

abstract:
  We study dual Abrikosov vortices in Abelian projected SU(2) gauge theory in
the Polyakov gauge. We show that vortices are present in this gauge but they
are suppressed with respect to the maximal Abelian gauge. We interpret this
difference in terms of the shielding of the electric charge by the charged
coset fields.


title: Redesigning Lattice QCD

abstract:
  There has been major progress in recent years in the development of improved
discretizations of the QCD action, current operators, etc for use in numerical
simulations that employ very coarse lattices. These lectures review the field
theoretic techniques used to design these discretizations, techniques for
testing and tuning the new formalisms that result, and recent simulation
results employing these formalisms.


title: Antiferromagnetism in four dimensions: search for non-triviality

abstract:
  We present antiferromagnetism as a mechanism capable of modifying
substantially the phase diagram and the critical behaviour of statistical
mechanical models. This is particularly relevant in four dimensions, due to the
connection between second order transition points and the continuum limit as a
quantum field theory. We study three models with an antiferromagnetic
interaction: the Ising and the O(4) Models with a second neighbour negative
coupling, and the $\RP{2}$ Model. Different conclusions are obtained depending
on the model.


title: The Phase Diagram of the Gonihedric 3d Ising Model via CVM

abstract:
  We use the cluster variation method (CVM) to investigate the phase structure
of the 3d gonihedric Ising actions defined by Savvidy and Wegner. The
geometrical spin cluster boundaries in these systems serve as models for the
string worldsheets of the gonihedric string embedded in ${\bf Z}^3$. The models
are interesting from the statistical mechanical point of view because they have
a vanishing bare surface tension. As a result the action depends only on the
angles of the discrete surface and not on the area, which is the antithesis of
the standard 3d Ising model.
  The results obtained with the CVM are in good agreement with Monte Carlo
simulations for the critical temperatures and the order of the transition as
the self-avoidance coupling $\kappa$ is varied. The value of the magnetization
critical exponent $\beta = 0.062 \pm 0.003$, calculated with the cluster
variation--Pad\`e approximant method, is also close to the simulation results.


title:
Critical exponents and unusual properties of the broken phase in the
  3d-RP(2) antiferromagnetic model

abstract:
  We present the results of a Monte Carlo simulation of the antiferromagnetic
RP(2) model in three dimensions. With finite-size scaling techniques we
accurately measure the critical exponents and compare them with those of O(N)
models. We are able to parameterize the corrections-to-scaling. The symmetry
properties of the broken phase are also studied.


title: Overlap for Majorana-Weyl fermions

abstract:
  The power of the overlap formalism is illustrated by regularizing theories
based on Majorana-Weyl fermions.


title: Overlap for 2D chiral U(1) models

abstract:
  The overlap formulation is applied to an anomaly free combination of chiral
fermions coupled to U(1) gauge fields on a 2D torus. Evidence is presented that
gauge averaging the overlap phases in these models produces correct continuum
results.


title: Fixed point action and topological charge for SU(2) gauge theory

abstract:
  We present a theoretically consistent definition of the topological charge
operator based on renormalization group arguments. Results of the
  measurement of the topological susceptibility at zero and finite temperature
for SU(2) gauge theory are presented.


title: QCD with chiral 4-fermion interactions ($\chi$QCD)

abstract:
  Lattice QCD with staggered quarks is augmented by the addition of a chiral
4-fermion interaction. The Dirac operator is now non-singular at $m_q=0$,
decreasing the computing requirements for light quark simulations by at least
an order of magnitude. We present preliminary results from simulations at
finite and zero temperatures for $m_q=0$, with and without gauge fields.


title: Scaling functions for O(4) in three dimensions

abstract:
  Monte Carlo simulation using a cluster algorithm is used to compute the
scaling part of the free energy for a three dimensional O(4) spin model. The
results are relevant for analysis of lattice studies of high temperature QCD.


title: Finite Temperature Lattice QCD with Clover Fermions

abstract:
  We report on our simulation of finite temperature lattice QCD with two
flavors of ${\cal O}(a)$ Symanzik-improved fermions and ${\cal O}(a^2)$
Symanzik-improved glue. Our thermodynamic simulations were performed on an $8^3
\times 4$ lattice, and we have performed complementary zero temperature
simulations on an $8^3 \times 16$ lattice. We compare our results to those from
simulations with two flavors of Wilson fermions and discuss the improvement
resulting from use of the improved action.


title: Random matrix model approach to chiral symmetry

abstract:
  We review the application of random matrix theory (RMT) to chiral symmetry in
QCD. Starting from the general philosophy of RMT we introduce a chiral random
matrix model with the global symmetries of QCD. Exact results are obtained for
universal properties of the Dirac spectrum: i) finite volume corrections to
valence quark mass dependence of the chiral condensate, and ii) microscopic
fluctuations of Dirac spectra. Comparisons with lattice QCD simulations are
made. Most notably, the variance of the number of levels in an interval
containing $n$ levels on average is suppressed by a factor $(\log n)/\pi^2 n$.
An extension of the random matrix model model to nonzero temperatures and
chemical potential provides us with a schematic model of the chiral phase
transition. In particular, this elucidates the nature of the quenched
approximation at nonzero chemical potential.


title: Monopole Condensation and Polyakov Loop in Finite-Temperature Pure QCD

abstract:
  We study the relation between the abelian monopole condensation and the
deconfinement phase transition of the finite-temperature pure QCD. The
expectation value of the monopole contribution to the Polyakov loop becomes
zero when a long monopole loop is distributed uniformly in the configuration of
the confinement phase. On the other hand, it becomes non-zero when the long
monopole loop disappears in the deconfinement phase. We also discuss the
relation between the monopole behaviors and the usual interpretation of the
spontaneous breaking of Z(N) symmetry in finite-temperature SU(N) QCD. It is
found that the boundary condition of the space direction is important to
understand the Z(N) symmetry in terms of the monopoles.


title:
The two-phase issue in the O(n) non-linear $\sigma$-model: A Monte Carlo
  study

abstract:
  We have performed a high statistics Monte Carlo simulation to investigate
whether the two-dimensional O(n) non-linear sigma models are asymptotically
free or they show a Kosterlitz- Thouless-like phase transition. We have
calculated the mass gap and the magnetic susceptibility in the O(8) model with
standard action and the O(3) model with Symanzik action. Our results for O(8)
support the asymptotic freedom scenario.


title: The phase structure of the 3-d Thirring model

abstract:
  We study the phase structure of the Thirring model in 3-d and find it to be
compatible with the existence of a non gaussian fixed point of RG. A Finite
Size Scaling argument is included in the equation of state in order to avoid
the assumptions usually needed to extrapolate to the thermodynamical limit.


title: Disorder Parameter of Confinement

abstract:
  The disorder parameter of confinement-deconfinement phase transition based on
the monopole action determined previously in $SU(2)$ QCD are investigated. We
construct an operator which corresponds to the order parameter defined in the
abelian Higgs model. The operator shows proper behaviors as the disorder
parameter in the numerical simulations of finite temperature QCD.


title: A Study of the Static-Light $B_B$ Parameter

abstract:
  We calculate the $B_B$ parameter, relevant for $\overline{B}^0$--$B^0$
mixing, from a lattice gauge theory simulation using the static approximation
for the heavy quark and the Wilson action for the light quark and gauge fields.
Improved sources, produced by an optimized variational technique, {\sc most},
reduce statistical errors and minimize excited-state contamination of the
ground-state signal. Renormalization of four-fermion operator coefficients,
using the Lepage-Mackenzie procedure for estimating typical momentum scales, is
linearized to reduce order $\alpha_s^2$ uncertainties.


title: The order of the phase transition in 3d U(1)+Higgs theory

abstract:
  We study the order of the phase transition in the 3d U(1)+Higgs theory, which
is the Ginzburg-Landau theory of superconductivity. We confirm that for small
scalar self-coupling the transition is of first order. For large scalar
self-coupling the transition ceases to be of first order, and a non-vanishing
scalar mass suggests that the transition may even be of higher than second
order.


title: Species doubling and effective Lagrangians

abstract:
  Coupling gauge fields to the chiral currents from an effective Lagrangian for
pseudoscalar mesons naturally gives rise to a species doubling phenomenon
similar to that seen with fermionic fields in lattice gauge theory.


title: Field strength correlators in QCD at zero and non-zero temperature

abstract:
  We study, by numerical simulations on a lattice, the behaviour of the
gauge--invariant field strength correlators in QCD both at zero temperature,
down to a distance of 0.1 fm, and at finite temperature, across the
deconfinement phase transition.


title: Field Strength and Monopoles in Dual U(1) Lattice Gauge Theory

abstract:
  In any Abelian gauge theory with an action periodic in the link variables one
can perform a duality transformation not only in the partition function, but
also in correlation functions including Polyakov loops. The calculation of
expectation values in the confinement phase, like electric field strength or
monopole currents in the presence of external charges, becomes significantly
more efficient simulating the dual theory. We demonstrate this using the
ordinary Wilson action. This approach also allows a quantitative analysis of
the dual superconductor model, because the dual transformed U(1) theory can be
regarded as limit of a dual non-compact Abelian Higgs model. In this way we
also try to interpret the behaviour of monopole condensate and string
fluctuations. Finally we present some applications for simulating the dual U(1)
gauge theory.


title: Finite Size Scaling Analysis with Linked Cluster Expansions

abstract:
  Linked cluster expansions are generalized from an infinite to a finite volume
on a $d$-dimensional hypercubic lattice. They are performed to 20th order in
the expansion parameter to investigate the phase structure of scalar $O(N)$
models for the cases of $N=1$ and $N=4$ in 3 dimensions. In particular we
propose a new criterion to distinguish first from second order transitions via
the volume dependence of response functions for couplings close to but not at
the critical value. The criterion is applicable to Monte Carlo simulations as
well. Here it is used to localize the tricritical line in a $\Phi^4 + \Phi^6$
theory. We indicate further applications to the electroweak transition.


title: A lattice formulation of chiral gauge theories

abstract:
  We present a method for implementing gauge theories of chiral fermions on the
lattice.


title: Instantons in the Maximally Abelian Gauge

abstract:
  We investigate the Maximally Abelian (MA) Projection for a single $SU(2)$
instanton in continuum gauge theory. We find that there is a class of solutions
to the differential MA gauge condition with circular monopole loops of radius
$R$ centered on the instanton of width $\rho$. However, the MA gauge fixing
functional $G$ decreases monotonically as $R/\rho \rightarrow 0$. Its global
minimum is the instanton in the singular gauge. We point out that interactions
with nearby anti-instantons are likely to excite these monopole loops.


title: Linked Cluster Expansions on non-trivial topologies

abstract:
  Linked cluster expansions provide a useful tool both for analytical and
numerical investigations of lattice field theories. The expansion parameter is
the interaction strength fields at neighboured lattice sites are coupled. They
result into convergent series for free energies, correlation functions and
susceptibilities. The expansions have been generalized to field theories at
finite temperature and to a finite volume. Detailed information on critical
behaviour can be extracted from the high order behaviour of the susceptibility
series. We outline some of the steps by which the 20th order is achieved.


title: Condensation of vortices in the X-Y model in 3d: a disorder parameter

abstract:
  A disorder parameter is constructed which signals the condensation of
vortices. The construction is tested by numerical simulations on lattice.


title: Improved action and Hamiltonian in finite volumes

abstract:
  We introduce a new Symanzik improved action by adding a 2x2 plaquette in such
a way that the Feynman rules in the covariant gauge simplify. We call this the
square Symanzik action. Some comparisons with the continuum and the standard
Wilson action are made in intermediate volumes, where mass ratios are
accurately known and the precise amount of improvement can be determined.
Ratios of the Lambda parameters will be presented, as well as partial results
for the one-loop improvement coefficients. We discuss some of the intricacies
that arise because of violations of unitarity at the scale of the cutoff. In
particular we show how a field redefinition in the zero-momentum effective
action allows one to remove scaling violations linear in the lattice spacing.


title: Four Quarks from Lattice to the Continuum

abstract:
  A continuum extrapolation of static four- and two-quark energies calculated
in quenched SU(2) is done based on Sommer's method of setting the scale. A
model for four-quark energies with explicit gluonic degrees of freedom removed
is fitted to these energies and the behavior of the parameters of the model is
investigated.


title: A Preliminary Lattice Study of the Glue in the Nucleon

abstract:
  About half the mass of a hadron is given from gluonic contributions. In this
talk we calculate the chromo-electric and chromo-magnetic components of the
nucleon mass. These computations are numerically difficult due to gluon field
ultra-violet fluctuations. Nevertheless a high statistics feasibility run using
quenched Wilson fermions seems to show reasonable signals.


title: Glueballs on S^3

abstract:
  For SU(2) gauge theory on the three-sphere we study the dynamics of the
low-energy modes. By explicitely integrating out the high-energy modes, the
one-loop correction to the hamiltonian for this problem is obtained. After
imposing the $\theta$-dependence through boundary conditions in configuration
space, we obtain the glueball spectrum of the effective theory with a
variational method.


title: Improved gluonic actions on anisotropic lattices

abstract:
  The use of novel perturbatively-improved gluonic actions on anisotropic
lattices in which the temporal spacing is much smaller than that in the spatial
directions is discussed. Such actions permit more efficient measurements of
noisy correlation functions, such as glueball correlators, on coarse lattices.
A derivation of these actions at tree-level is outlined; mean-field link
renormalization plays a crucial role in their construction. Results for the
low-lying glueball masses and the heavy-quark potential are presented.


title: Non-Reversibility of Molecular Dynamics Trajectories

abstract:
  We study the non-reversibility of molecular dynamics trajectories arising
from the amplification of rounding errors. We analyse the causes of such
behaviour and give arguments, indicating that this does not pose a significant
problem for Hybrid Monte Carlo computations. We present data for pure SU(3)
gauge theory and for QCD with dynamical fermions on small lattices to
illustrate and to support some of our ideas.


title:
Comparing Wilson and Clover Quenched $SU(3)$ Spectroscopy with an
  Improved Gauge Action

abstract:
  We present results of quenched $SU(3)$ hadron spectroscopy comparing
$\order(a)$ improved Wilson (Clover) fermions with conventional Wilson
fermions. The configurations were generated using an $\order(a^2)$ improved
6-link $SU(3)$ pure gauge action at $\beta$'s corresponding to lattice spacings
of $0.15$, $0.18$, $0.20$, $0.33$, and $0.43$ fm. We find evidence that
fermionic scaling violations are consistent with $\order(a^2)$ for Clover and
$\order(a)$ with a nonnegligible $\order(a^2)$ term for standard Wilson
fermions. This latter mixed ansatz makes a reliable continuum extrapolation
problematic for Wilson fermions. We also find that the slope of the scaling
violations is roughly $250 MeV$ for both Wilson and Clover fermions.


title:
Spin-spin correlation functions of spin systems coupled to 2-d quantum
  gravity for $0 < c < 1$

abstract:
  We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces
coupled to Ising and three--states Potts model matter. By measuring spin-spin
correlation functions as a function of the geodesic distance we provide
substantial evidence for a diverging correlation length at $\beta_c$. The
corresponding scaling exponents are directly related to the KPZ exponents of
the matter fields as conjectured in [4] (NPB454(1995)313).


title: A Two-Parameter Recursion Formula For Scalar Field Theory

abstract:
  We present a two-parameter family of recursion formulas for scalar field
theory. The first parameter is the dimension $(D)$. The second parameter
($\zeta$) allows one to continuously extrapolate between Wilson's approximate
recursion formula and the recursion formula of Dyson's hierarchical model. We
show numerically that at fixed $D$, the critical exponent $\gamma $ depends
continuously on $\zeta$. We suggest the use of the $\zeta -$independence as a
guide to construct improved recursion formulas.


title: Wilson Fermions at finite temperature

abstract:
  I conjecture on the phase structure expected for lattice gauge theory with
two flavors of Wilson fermions, concentrating on large values of the hopping
parameter. Numerous phases are expected, including the conventional confinement
and deconfinement phases, as well as an Aoki phase with spontaneous breaking of
flavor and parity and a large hopping phase corresponding to negative quark
masses.


title:
The Oscillatory Behavior of the High-Temperature Expansion of Dyson's
  Hierarchical Model: A Renormalization Group Analysis

abstract:
  We calculate 800 coefficients of the high-temperature expansion of the
magnetic susceptibility of Dyson's hierarchical model with a Landau-Ginzburg
measure. Log-periodic corrections to the scaling laws appear as in the case of
a Ising measure. The period of oscillation appears to be a universal quantity
given in good approximation by the logarithm of the largest eigenvalue of the
linearized RG transformation, in agreement with a possibility suggested by K.
Wilson and developed by Niemeijer and van Leeuwen. We estimate $\gamma $ to be
1.300 (with a systematic error of the order of 0.002) in good agreement with
the results obtained with other methods such as the $\epsilon $-expansion. We
briefly discuss the relationship between the oscillations and the zeros of the
partition function near the critical point in the complex temperature plane.


title: Thermodynamics for two flavor QCD

abstract:
  We conclude our analysis of the N_t=6 equation of state for two flavor QCD,
first described at last year's conference. We have obtained new runs at
am_q=0.025 and improved runs at am_q=0.0125. The results are extrapolated to
m_q=0, and we extract the speed of sound as well. We also present evidence for
a restoration of the SU(2) X SU(2) chiral symmetry just above the crossover,
but not of the axial U(1) chiral symmetry.


title: Phase transition and topology in 4d simplicial gravity

abstract:
  We present data indicating that the recent evidence for the phase transition
being of first order does not result from a breakdown of the ergodicity of the
algorithm. We also present data showing that the thermodynamical limit of the
model is independent of topology.


title: Lattice Fermions and Chiral Symmetry

abstract:
  We propose a formulation of lattice fermions with one-sided differences that
is hermitian, chirally symmetric (barring a bare mass term) and completely free
of doubling. To obtain the axial anomaly in perturbation theory it was
necessary to break chiral symmetry on the lattice only through a bare mass term
for the physical fermion. The chiral limit may be taken once the continuum
limit is reached. We comment on the role of the mass term with examples
elsewhere in field theory.


title: Correlations in fluctuating geometries

abstract:
  We compare two definitions of connected correlation functions in fluctuating
geometries. We show results of the MC simulations for 4D dynamical
triangulation in the elongated phase and compare them with the exact
calculations of correlation functions in the branched polymer model.


title: Appearence of Mother Universe and Singular Vertices in Random Geometries

abstract:
  We discuss a general mechanism that drives the phase transition in the
canonical ensemble in models of random geometries. As an example we consider a
solvable model of branched polymers where the transition leading from tree- to
bush-like polymers relies on the occurrence of vertices with a large number of
branches. The source of this transition is a combination of the constraint on
the total number of branches in the canonical ensemble and a nonlinear
one-vertex action. We argue that exactly the same mechanism, which we call
constrained mean-field, plays the crucial role in the phase transition in 4d
simplicial gravity and, when applied to the effective one-vertex action,
explains the occurrence of both the mother universe and singular vertices at
the transition point when the system enters the crumpled phase.


title: Monte-Carlo study of the $\Delta\rho$ parameter

abstract:
  We present results concerning a lattice study of the electroweak
$\rho$-parameter. We have used an SU(2)$\times$U(1) symmetric chiral Yukawa
model built with Zaragoza fermions. The decoupling of the species doublers in
this model is verified numerically. We find that the numerical data for
$\Delta\rho$ are well described by one-loop perturbation theory with the same
finite volume and with the same finite cut-off. However, a finite cut-off can
cause substantial deviations of $\Delta\rho$ from the standard value, even in
infinite volume.


title: Topology by improved cooling: susceptibility and size distributions

abstract:
  We use a cooling algorithm based on an improved action with scale invariant
instanton solutions, which needs no monitoring or calibration and has a
inherent cut off for dislocations. We present results for SU(2) Yang-Mills
theory where the method provides good susceptibility data and physical size
distributions of instantons.


title: Perturbative renormalization of bilinear quark and gluon operators

abstract:
  The renormalisation constants for local bilinear quark operators are
calculated using the Sheikholeslami-Wohlert improved action. In addition we
compute the renormalisation constant of the leading gluon operator for
different group representations and discuss the mixing of the operators E^2 and
B^2.


title:
Quenched Light Hadron Spectrum and Decay Constants using Improved Wilson
  Fermion Actions

abstract:
  We compare results obtained using the Sheikholeslami-Wohlert (SW) fermion
action with tree-level and tadpole-improved coefficients for $5.7\le\beta\le
6.2$.


title: Confining Classical Configurations

abstract:
  We construct a family of smooth, almost self-dual, non-thermalized SU(2)
gauge field configurations, and measure the average of the fundamental, adjoint
and spin $\frac{3}{2}$ representation Wilson loops on them. We get area law in
all three cases. We also study thermalised configurations at $\beta= 2.325$
after cooling. The ratio of string tension in the spin j representation over
that in the fundamental, stays constant with cooling.


title: A Monte Carlo study of old, new and tadpole improved actions

abstract:
  Scaling of mass ratios in intermediate volumes, obtained with improved SU(2)
lattice actions is tested against analytic results for the Wilson and continuum
action. A new improved action is introduced by adding a 2X2 plaquette to the
Symanzik action. Completing a square leads to a covariant propagator that
simplifies perturbative calculations. Data is presented on lattices of size
4**3X128, with lattice spacings of approximately 0.02 and 0.12 fermi. For the
latter case no further improvement as compared to the tree-level action was
observed when including the Lepage-Mackenzie tadpole correction to the one-loop
improved Luscher-Weisz Symanzik action.


title: Visualization of topological objects in QCD

abstract:
  Recently evidence appeared that instantons and monopoles have a certain local
correlation in four-dimensional pure $SU(2)$ and $SU(3)$ gauge theory. We
visualize several specific gauge field configurations and show directly that
there is an enhanced probability for finding maximally projected abelian
monopole loops in the vicinity of instantons. This feature is independent of
the topological charge definition used.


title:
Correlation functions between topological objects -- field theoretic
  versus geometric definitions

abstract:
  We analyze topological objects in pure gluonic $SU(2)$ lattice gauge theory
and compute correlation functions between instantons and monopoles. Concerning
the instantons we use geometric and field theoretic definitions of the
topological charge. On a $12^3\times 4$ lattice it turns out that topological
quantities have a non-trivial local correlation. The auto-correlation functions
of the topological charge depend on cooling for both definitions. We fit the
correlation functions to exponentials and obtain screening masses.


title:
B Physics on the Lattice: $\overline{\Lambda}$, $\lambda_{1}$,
  $\overline{m}_{b}(\overline{m}_{b})$, $\lambda_2$, $B^{0}-\bar{B}^{0}$
  mixing, $\fb$ and all that

abstract:
  We present a short review of our most recent high statistics lattice
determinations in the HQET of the following important parameters in B physics:
the B--meson binding energy, $\overline{\Lambda}$ and the kinetic energy of the
b quark in the B meson, $\lambda_1$, which due to the presence of power
divergences require a non--perturbative renormalization to be defined; the
$\overline{MS}$ running mass of the b quark,
$\overline{m}_{b}(\overline{m}_{b})$; the $B^{*}$--$B$ mass splitting, whose
value in the HQET is determined by the matrix element of the chromo--magnetic
operator between B meson states, $\lambda_2$; the B parameter of the
$B^{0}$--$\bar{B}^{0}$ mixing, $B_{B}$, and the decay constant of the B meson,
$f_{B}$. All these quantities have been computed using a sample of $600$ gauge
field configurations on a $24^{3}\times 40$ lattice at $\beta=6.0$. For
$\overline{\Lambda}$ and $\overline{m}_{b}(\overline{m}_{b})$, we obtain our
estimates by combining results from three independent lattice simulations at
$\beta=6.0$, $6.2$ and $6.4$ on the same volume.


title:
Evaluating Sea Quark Contributions to Flavour-Singlet Operators in
  Lattice QCD

abstract:
  In a full QCD lattice study with $N_f = 2$ Wilson fermions, we seek to
optimize the signals for the disconnected contributions to the matrix element
of flavour-singlet operators between nucleon states, which are indicative for
sea quark effects. We demonstrate, in form of a fluctuation analysis to the
noisy estimator technique, that -- in order to achieve a tolerable signal to
noise-ratio in full QCD -- it is advantageous to work with a $Z_2$-noise source
rather than to rely only on gauge invariance to cancel non-gauge-invariant
background. In the case of the $\pi$N $\sigma$-term, we find that 10
$Z_2$-noise sources suffice on our sample ( about 150 independent QCD
configurations at $\beta = 5.6$ on $16^3\times32$ with $\kappa_{sea} = 0.157$,
equivalent to $M_{\pi}/M_{\rho} = 0.76(1)$), to achieve decent signals and
adequate fluctuations, rather than 300 such sources as recently used in
quenched simulations.


title: Laplacian Abelian Projection

abstract:
  A new partial gauge fixing condition for the abelian projection is
introduced. It is based on the lowest-lying eigenvector of a covariant
Laplacian operator. This gauge is smooth and free of lattice Gribov copies.
These properties are important for an unambiguous computation of the abelian
projected gauge field configuration.


title: Simplicial Gravity in Dimension Greater than Two

abstract:
  We consider two issues in the DT model of quantum gravity. First, it is shown
that the triangulation space for D>3 is dominated by triangulations containing
a single singular (D-3)-simplex composed of vertices with divergent dual
volumes. Second we study the ergodicity of current simulation algorithms.
Results from runs conducted close to the phase transition of the
four-dimensional theory are shown. We see no strong indications of ergodicity
br eaking in the simulation and our data support recent claims that the
transition is most probably first order. Furthermore, we show that the critical
properties of the system are determined by the dynamics of remnant singular
vertices.


title:
Multicanonical Study of Continuum Physics in the D=2 $O(3)$ Nonlinear
  Sigma Model

abstract:
  Employing a variant of the Multicanonical Ensemble we study twisted spin
configurations on periodic boxes in the $D=2$ $O(3)$ nonlinear sigma model for
$\beta$-values inbetween $1.55$ to $3.1$. The free energy difference of twisted
spin configurations is determined from the constraint effective potential. The
finite size scaling behavior is in accordance with the asymptotically free
nature of the continuum theory. Upon certain reasonable assumptions we
determine the $\Delta \beta( \beta)$-shift of the stiffness correlation length
$\xi_s$. The mass-gap as determined by our analysis is
${m_0}=79.6(1.9)~\Lambda_{latt}$. This value agrees with the analytical result
of the thermodynamic Bethe Ansatz ${m_0}=80.1~\Lambda_{latt}$.


title: The flat phase of fixed-connectivity membranes

abstract:
  The statistical mechanics of flexible two-dimensional surfaces (membranes)
appears in a wide variety of physical settings. In this talk we discuss the
simplest case of fixed-connectivity surfaces. We first review the current
theoretical understanding of the remarkable flat phase of such membranes. We
then summarize the results of a recent large scale Monte Carlo simulation of
the simplest conceivable discrete realization of this system \cite{BCFTA}. We
verify the existence of long-range order, determine the associated critical
exponents of the flat phase and compare the results to the predictions of
various theoretical models.


title: Finite-element quantum field theory

abstract:
  An alternative approach to lattice gauge theory has been under development
for the past decade. It is based on discretizing the operator Heisenberg
equations of motion in such a way as to preserve the canonical commutation
relations at each lattice site. It is now known how to formulate a non-Abelian
gauge theory within this framework. The formulation appears to be free of
fermion doubling. Since the theory is unitary, a time-development operator
(Hamiltonian) can be constructed.


title: Lattice computation of structure functions

abstract: Recent lattice calculations of hadron structure functions are described.


title: QCD Thermodynamics with Improved Actions

abstract:
  The thermodynamics of the SU(3) gauge theory has been analyzed with tree
level and tadpole improved Symanzik actions. A comparison with the continuum
extrapolated results for the standard Wilson action shows that improved actions
lead to a drastic reduction of finite cut-off effects already on lattices with
temporal extent $N_\tau=4$. Results for the pressure, the critical temperature,
surface tension and latent heat are presented. First results for the
thermodynamics of four-flavour QCD with an improved staggered action are also
presented. They indicate similarly large improvement factors for bulk
thermodynamics.


title: Low-Lying Eigenvalues of the Wilson-Dirac Operator

abstract:
  An exploratory study of the low-lying eigenvalues of the Wilson-Dirac
operator and their corresonding eigenvectors is presented. Results for the
eigenvalues from quenched and unquenched simulations are discussed. The
eigenvectors are studied with respect to their localization properties in the
quenched approximation for the cases of SU(2) and SU(3).


title: Some new results in O(a) improved lattice QCD

abstract:
  It is shown how on-shell O(a) improvement can be implemented
non-perturbatively in lattice QCD with Wilson quarks. Improvement conditions
are obtained by requiring the PCAC relation to hold exactly in certain matrix
elements. These are derived from the QCD Schr\"odinger functional which enables
us to simulate directly at vanishing quark masses. In the quenched
approximation and for bare couplings in the range $0\leq g_0\leq 1$, we
determine the improved action, the improved axial current, the additive
renormalization of the quark mass and the isospin current normalization
constants Z_A and Z_V.


title: SU(3) glueballs on coarse, anisotropic lattices

abstract:
  Results from a calculation of the low-lying glueball spectrum of pure-gauge
SU(3) are used as a test of the effectiveness of improved discretisation
schemes in reducing finite spacing errors. Glueball masses are extracted from
simulations on anisotropic lattices, where the temporal lattice spacing is much
shorter than the spatial ones. This allows clearer resolution of the decay of
glueball correlators.


title: Study of Critical Slowing-Down in $SU(2)$ Landau Gauge Fixing

abstract:
  We study the problem of critical slowing-down for gauge-fixing algorithms
(Landau gauge) in $SU(2)$ lattice gauge theory on $2$ and $4$ dimensional
lattices, both numerically and analytically. We consider five such algorithms,
and we measure four different observables. A detailed discussion and analysis
of the tuning of these algorithms is also presented.


title: Transport Coefficients of Quark Gluon Plasma for Pure Gauge Models

abstract:
  The transport coefficients of quark gluon plasma are calculated on a lattice
16**3X8, with the pure gauge models. Matsubara Green's functions of energy
momentum tensors have very large fluctuations and about a few million MC sweeps
are needed to reduce the errors reasonably small in the case of the standard
action. They are much suppressed if Iwasaki's improved action is employed.
Preliminary results show that the transport coefficients roughly depend on the
coupling constant as a**(-3)(g) in the case of SU(2).


title:
Dynamical Wilson fermions and the problem of the chiral limit in compact
  lattice QED

abstract:
  We compare the approach to the chiral transition line $~\kappa_c(\bt)~$ in
quenched and full compact lattice QED with Wilson fermions within the
confinement phase, especially in the pseudoscalar sector of the theory. We show
that in the strong coupling limit ($\beta =0$) the quenched theory is a good
approximation to the full one, in contrast to the case of $\beta =0.8$. At the
larger $\beta$-value the transition in the full theory is inconsistent with the
zero--mass limit of the pseudoscalar particle, thus prohibiting the definition
of a chiral limit.


title: Abelian dominance and adjoint color sources

abstract:
  Abelian dominance in the case of color sources in the fundamental
representation is shown to follow from certain properties of maximal abelian
projected SU(2) gauge theory. The possibility of having an analog of abelian
dominance in the case of adjoint representation sources is addressed in the
same framework.


title: Correlation functions in lattice formulations of quantum gravity

abstract:
  We compare different models of a quantum theory of four-dimensional lattice
gravity based on Regge's original proposal. From Monte Carlo simulations we
calculate two-point functions between geometrical quantities and estimate the
masses of the corresponding interaction particles.


title: Fixed-point action for fermions in QCD

abstract:
  We report our progress constructing a fixed-point action for fermions
interacting with SU(3) gauge fields.


title: Phase Structure of Lattice QCD at Finite Density with Dynamical Fermions

abstract:
  We compare the chemical potential associated with the onset of non-zero
baryon number density on $6^4$ and $8^4$ lattices at $\beta=5.1$ and ma=0.01.
We provide evidence for $Z(3)$ tunnelling. We determine a critical chemical
potential of $\mu a \simeq 0.1$ which is unexpectedly low. We also determine
the dependence of the onset of the observed phase transition on the quark mass.
The physically misleading result of the quenched theory is shown to persist
despite the inclusion of the complex fermion determinant.


title: Quarkonium Physics and $\alpha_{strong}$ from Quarkonia

abstract:
  Recent results in Quarkonia are reviewed, including updates on spectroscopy
and $\alpha_s$, and a first look at quarkonium annihilation decays.


title: SU(3) lattice gauge autocorrelations with anisotropic action

abstract:
  We report results of autocorrelation measurements in pure $SU(3)$ lattice
gauge theory. The computations are performed on the {\sc convex spp1200}
parallel platform within the {\sc canopy} programming environment. The focus of
our analysis is on typical autocorrelation times and optimization of the mixing
ratio between overrelaxation and pseudo-heatbath sweeps for generating gauge
field configurations. We study second order tadpole-improved approximations of
the Wilson action in the gluon sector, which offers the advantage of working on
smaller lattices ($8^3~\times~16$ and $6^3~\times$~12~--~30). We also make use
of anisotropic lattices, with temporal lattice spacing smaller than the spatial
spacing, which prove useful for calculating noisy correlation functions with
large spatial lattice discretization (of the order of 0.4 fm).


title: Extended instantons generated on the lattice

abstract:
  We have been able to observe directly extended instantons on the lattice,
with a new method that does not require dislocations to measure them, and where
we do not perform cooling. We showed, based on the simple Abelian Higgs model
in $1+1$ dim., that one can extract the instanton and anti-instanton density
and their size, by measuring the topological charge, $Q_v$ , on sub-volumes $v$
larger than the instanton sizes, but smaller than the periodic lattice of size
$V$. We are working on the generalization for non-abelian models.


title:
Four-dimensional Simulation of the Hot Electroweak Phase Transition with
  the SU(2) Gauge-Higgs Model

abstract:
  We study the finite-temperature phase transition of the four-dimensional
SU(2) gauge-Higgs model for intermediate values of the Higgs boson mass in the
range $50 \lsim m_H \lsim 100$GeV on a lattice with the temporal lattice size
$N_t=2$. The order of the transition is systematically examined using finite
size scaling methods. Behavior of the interface tension and the latent heat for
an increasing Higgs boson mass is also investigated.


title: Scaling topological charge in the CP^3 model using a fixed point action

abstract:
  We define a fixed point action in two-dimensional lattice CP^{N-1} models.
The fixed point action is a classical perfect lattice action, which is expected
to show strongly reduced cut-off effects in numerical simulations. Furthermore,
the action has scale invariant instanton solutions, which enables us to define
a topological charge without topological defects. We present results for the
scaling of the topological suceptibility from a Monte Carlo simulation in the
CP^3 model.


title:
The effect of tree-level and mean-field improvement on the light-hadron
  spectrum in quenched QCD

abstract:
  We compute the light hadron mass spectrum at beta=5.7 using the O(a) improved
Sheikholeslami-Wohlert (SW) fermion action with two choices of the clover
coefficient: the classical value, c=1, and a mean-field or tadpole-improved
estimate c=1.57. We compare our results with those of the GF11 Collaboration
who use the Wilson fermion action (c=0). We find that changing c from zero to 1
and 1.57 leads to significant differences in the masses of the chirally
extrapolated and strange pseudoscalar and vector mesons, the nucleon, the
Delta, and also in the Edinburgh plot. A number of other quantities, for
example m_V^2-m_PS^2, J, am_K/am_\rho and am_{K^*}/am_\rho do not appear to
change significantly. We also investigate the effect of changing the lattice
volume from approximately (2 fm)^3 to (2.6 fm)^3. We find that the meson masses
are consistent to within one standard deviation and baryon masses are
consistent to within two standard deviations.


title: Latest Results from the SGO Collaboration

abstract:
  We present results for the spectrum and decay constants of B mesons from
NRQCD using dynamical configurations at $\beta=5.6$ with two flavours of
staggered fermions. The light quarks are generated using the Clover action with
tadpole improvement.


title: Forces between composite particles in QCD

abstract:
  Starting from the meson-meson Green function in 3+1 dimensional quenched
lattice QCD we calculate potentials between heavy-light mesons for various
light-quark mass parameters. For the valence quarks we employ the staggered
scheme. The resulting potentials turn out to be short ranged and attractive. A
comparison with a tadpole improved action for the gauge fields is presented.


title: A Parallel SSOR Preconditioner for Lattice QCD

abstract:
  A parallelizable SSOR preconditioning scheme for Krylov subspace iterative
solvers in lattice QCD applications involving Wilson fermions is presented. In
actual Hybrid Monte Carlo and quark propagator calculations it helps to reduce
the number of iterations by a factor of 2 compared to conventional odd-even
preconditioning. This corresponds to a gain in cpu-time of 30\% - 70\% over
odd-even preconditioning.


title:
Mass Spectrum of the 3d SU(2) Higgs Model and the Symmetric Electroweak
  Phase

abstract:
  We present results for the masses of the low-lying states with quantum
numbers $0^{++}$, $2^{++}$ and $1^{--}$ as well as Polyakov line correlations
in the Higgs and confinement regions of the 3d SU(2) Higgs model. In the
confinement phase we find a dense spectrum of bound states approximately split
into two disjoint sectors. One consists of W-balls nearly identical to the
glueball spectrum of the pure gauge theory, the other of bound states of
scalars.


title: Progress on Perfect Lattice Actions for QCD

abstract:
  We describe a number of aspects in our attempt to construct an approximately
perfect lattice action for QCD. Free quarks are made optimally local on the
whole renormalized trajectory and their couplings are then truncated by
imposing 3-periodicity. The spectra of these short ranged fermions are
excellent approximations to continuum spectra. The same is true for free
gluons. We evaluate the corresponding perfect quark-gluon vertex function,
identifying in particular the ``perfect clover term''. First simulations for
heavy quarks show that the mass is strongly renormalized, but again the
renormalized theory agrees very well with continuum physics. Furthermore we
describe the multigrid formulation for the non-perturbative perfect action and
we present the concept of an exactly (quantum) perfect topological charge on
the lattice.


title: Calculation of Moments of Nucleon Structure Functions

abstract:
  Preliminary results are presented in our program to calculate low moments of
structure functions for the proton and neutron on a $24^3\times32$ lattice at
$\beta=6.2$. A comparison is made for a variety of smeared nucleon sources and
preliminary results for the calculation of the nucleon tensor charge are
presented.


title: Scalar Quarkonium and the Scalar Glueball

abstract:
  Valence approximation glueball mass and decay calculations support the
identification of $f_J(1710)$ as the lightest scalar glueball. An alternate
glueball candidate is $f_0(1500)$. I present evidence for the identification of
$f_0(1500)$ as $s\overline{s}$ quarkonium.


title: Scalar Quarkonium Masses

abstract:
  We evaluate the valence approximation to the mass of scalar quarkonium for a
range of different parameters. Our results strongly suggest that the infinite
volume continuum limit of the mass of $s\overline{s}$ scalar quarkonium lies
well below the mass of $f_J(1710)$. The resonance $f_0(1500)$ appears to the
best candidate for $s\overline{s}$ scalar quarkonium.


title:
Monte Carlo computation of the effective potential for the three
  dimensional Ising system

abstract:
  Using a novel finite size scaling Monte Carlo technique, we calculate the
four, six and eight point renormalized coupling constants defined at zero
momentum for the three dimensional Ising system. Our values of the six and
eight point coupling constants are significantly different from those obtained
from other methods.


title:
Two-flavour Schwinger model with dynamical fermions in the L\"uscher
  formalism

abstract:
  We report preliminary results for 2D massive QED with two flavours of Wilson
fermions, using the Hermitean variant of L\"uscher's bosonization technique.
The chiral condensate and meson masses are obtained. The simplicity of the
model allows for high statistics simulations close to the chiral and continuum
limit, both in the quenched approximation and with dynamical fermions.


title:
Linear systems solvers - recent developments and implications for
  lattice computations

abstract:
  We review the numerical analysis' understanding of Krylov subspace methods
for solving (non-hermitian) systems of equations and discuss its implications
for lattice gauge theory computations using the example of the Wilson fermion
matrix. Our thesis is that mature methods like QMR, BiCGStab or restarted GMRES
are close to optimal for the Wilson fermion matrix. Consequently,
preconditioning appears to be the crucial issue for further improvements.


title: Aharonov--Bohm Effect in 3D Abelian Higgs Theory

abstract:
  We study a field--theoretical analogue of the Aharonov--Bohm effect in the 3D
Abelian Higgs Model: the corresponding topological interaction is proportional
to the linking number of the vortex and the particle world trajectories. We
show that the Aharonov--Bohm effect gives rise to a nontrivial interaction of
tested charged particles.


title: Suppressing Curvature Fluctuations in Dynamical Triangulations

abstract:
  We study numerically the dynamical triangulation formulation of
two-dimensional quantum gravity using a restricted class of triangulation,
so-called minimal triangulations, in which only vertices of coordination number
5, 6, and 7 are allowed. A real-space RG analysis shows that for pure gravity
(central charge c = 0) this restriction does not affect the critical behavior
of the model. Furthermore, we show that the critical behavior of an Ising model
coupled to minimal dynamical triangulations (c = 1/2) is still governed by the
KPZ-exponents.


title: Blocking of Dynamical Triangulations with Matter

abstract:
  We use the recently proposed node decimation algorithm for blocking dynamical
geometries to investigate a class of models, with central charge greater than
unity, coupled to 2D gravity. We demonstrate that the blocking preserves the
fractal structure of the surfaces.


title: Domain Wall Fermions and MC Simulations of Vector Theories

abstract:
  It is known that domain wall fermions may be used in MC simulations of vector
theories. The practicality and usefulness of such an implementation is
investigated in the context of the vector Schwinger model, on a 2+1 dimensional
lattice. Preliminary results of a Hybrid Monte Carlo simulation are presented.


title: Finite T Electroweak Phase Transition on the Lattice

abstract:
  This talk reviews recent lattice results on the high $T$ electroweak phase
transition. A remarkably accurate picture emerges: a) the transition is of
first order for $m_H \lsim 80$GeV and vanishes for larger $m_H$; b) transition
temperature, latent heat and interface tension are known, as well as c) the
properties of the broken and symmetric phases. New developments in the
sphaleron rate calculations are discussed.


title: Absence of Physical Walls in Hot Gauge Theories

abstract:
  This paper shows that there are no physical walls in the deconfined,
high-temperature phase of Z(2) lattice gauge theory. In a Hamiltonian
formulation, the interface in the Wilson lines is not physical. The line
interface and its energy are interpreted in terms of physical variables. They
are associated with a difference between two partition functions. One includes
only the configurations with even flux across the interface. The other is
restricted to odd flux.


title: First results with non-perturbative fermion improvement

abstract:
  We present initial results for light hadron masses and nucleon structure
functions using a recent proposal for eliminating all $O(a)$ effects from
Wilson fermion simulations in the quenched approximation. With initially
limited statistics, we find a much more linear APE plot and a value of the
axial coupling $g_A$ nearer to the experimental point than with comparable runs
using unimproved Wilson fermions.


title:
Remarks on the quantum gravity interpretation of 4D dynamical
  triangulation

abstract:
  We review some of the phenomenology in 4D dynamical triangulation and explore
its interpretation in terms of a euclidean effective action of the continuum
form $\intx \sqrt{g} [\mu -\frac{1}{16\pi G} R + \cdots]$.


title: Light Spectrum and Decay Constants in Full QCD with Wilson Fermions

abstract:
  We present results from an analysis of the light spectrum and the decay
constants f_{\pi} and f_V^{-1} in Full QCD with n_f=2 Wilson fermions at a
coupling of beta=5.6 on a 16^3x32 lattice.


title: Clustering of Monopoles in the Instanton Vacuum

abstract:
  We generate a random instanton vacuum with various densities and size
distributions. We perform numerically the maximally abelian gauge fixing of
these configurations in order to find monopole trajectories induced by
instantons. We find that instanton-induced monopole loops form enormous
clusters occupying the whole physical volume, provided instantons are
sufficiently dense. It indicates that confinement might be caused by
instantons.


title:
Improvements for Vachaspati-Vilenkin-type Algorithms for Cosmic String
  and Disclination Formation

abstract:
  We derive various consistency requirements for Vachaspati-Vilenkin type
Monte-Carlo simulations of cosmic string formation or disclination formation in
liquid crystals. We argue for the use of a tetrakaidekahedral lattice in such
simulations. We also show that these calculations can be carried out on
lattices which are formally infinite, and do not necessitate the specification
of any boundary conditions. This way string defects can be traced up to much
larger lengths than on finite lattices. The simulations then fall into a more
general class of simulations of self-interacting walks, which occupy the
underlying lattice very sparsely. An efficient search algorithm is essential.
We discuss various search strategies, and demonstrate how to implement hash
tables with collision resolution by open addressing. The time to trace a string
defect is then proportional only to the string length.


title: Instanton Distribution in Quenched and Full QCD

abstract:
  In order to optimize cooling as a technique to study the instanton content of
the QCD vacuum, we have studied the effects of alternative algorithms, improved
actions and boundary conditions on the evolution of single instantons and
instanton anti-instanton pairs. Using these results, we have extracted and
compared the instanton content of quenched and full QCD.


title:
Critical Higgs Mass and Temperature Dependence of Gauge Boson Masses in
  the SU(2) Gauge-Higgs Model

abstract:
  We study the effective 3-D SU(2) Gauge-Higgs model at finite temperature for
Higgs-masses in the range from $60$ GeV up to $100$ GeV. The first order
electroweak phase transition weakens with increasing Higgs-mass and terminates
at a critical end-point. For Higgs-mass values larger than about
$m_{H,c}=75.4(6)$ GeV the thermodynamic signature of the transition is
described by a crossover. Close to this Higgs-mass value we investigate the
vector boson propagator in Landau gauge. The calculated W-boson screening
masses are compared with predictions based on gap equations.


title: Assorted weak matrix elements involving the bottom quark

abstract:
  As part of a larger project to estimate the fB decay constant, we are
recalculating fB_static using a variational smearing method in an effort to
improve accuracy. Preliminary results for the static B_B parameter and HQET two
point functions are also presented.


title: Numerical Study of $ K^0$--$\bar{K}^0$ Mixing and $ B_K $

abstract:
  We have computed $ B_K $ with staggered fermions, using two different
methods: both in the one spin trace form and two spin trace form. Renormalized
results in both forms are in good agreement. The numerical simulations were
performed on a $ 16^3 \times 40 $ lattice in full QCD with $ \beta = 5.7 $. We
also tried an improved wall source method in order to select only the
pseudo-Goldstone bosons and compare the numerical results obtained with those
from the conventional wall source method. We have studied $ B_K $ with a series
of non-degenerate quark anti-quark pairs and saw no effect on $ B_K $, although
dramatic effects in the chiral limit were seen on the individual terms making
up $ B_K $.


title:
Scaling of the critical temperature and quark potential with a
  renormalization group improved SU(3) gauge action

abstract:
  We study the scaling property of the ratio of the critical temperature $T_c$
to the square root of the string tension $\sigma$ in the SU(3) pure gauge
theory using a renormalization group improved action. We first determine the
critical coupling $\beta_c$ on lattices with temporal extension $N_t=4$ and 6,
and then calculate the static quark potential at the critical couplings on
lattices at zero temperature. The values of $T_{c}/\sqrt{\sigma}$ in the
infinite volume limit are identical within errors, while they are slightly
larger than the value extrapolated to the continuum limit with the standard
action. We also note that the rotational invariance of the static quark
potential is remarkably restored in the both cases, and that the potential
$V(R)$ in physical units scales in the whole region of $R$ investigated.


title:
Chiral corrections to the axial charges of the octet baryons from
  quenched QCD

abstract:
  We calculate one-loop correction to the axial charges of the octet baryons
using quenched chiral perturbation theory, in order to understand chiral
behavior of the axial charges in quenched approximation to quantum
chromodynamics (QCD). In contrast to regular behavior of the full QCD chiral
perturbation theory result, $c_0+c_{l2}m_\pi^2\,\ln{m_\pi^2}+\cdots$, we find
that the quenched chiral perturbation theory result,
$c_0^Q+(c_{l0}^Q+c_{l2}^Qm_\pi^2)\ln{m_\pi^2}+c_2^Q m_\pi^2+\cdots$, is
singular in the chiral limit.


title: Update on $f_B$

abstract:
  We describe the current status of the MILC collaboration computation of
$f_B$, $f_{B_s}$, $f_D$, $f_{D_s}$ and their ratios. Progress over the past
year includes: better statistics and plateaus at $\beta=6.52$ (quenched),
$\beta=5.6$ ($N_F=2$) and $\beta=5.445$ ($N_F=2$), new runs with a wide range
of dynamical quark masses at $\beta=5.5$ ($N_F=2$), an estimate of the
systematic errors due to the chiral extrapolation, and an improved analysis
which consistently takes into account both the correlations in the data at
every stage and the systematic effects due to changing fitting ranges.


title: Fast Fermion Monte Carlo

abstract:
  Three possibilities to speed up the Hybrid Monte Carlo algorithm are
investigated. Changing the step-size adaptively brings no practical gain. On
the other hand, substantial improvements result from using an approximate
Hamiltonian or a preconditioned action.


title: Search for Effective Lattice Action of Pure QCD

abstract:
  We study a coupling flow of pure QCD gauge system by using the Monte Carlo
Renormalization Group method. A rough location of the renormalized trajectory
in two coupling space is obtained. Also we compare 4 different actions;
(a)standard Wilson, (b)Symanzik's, (c)Iwasaki's and (d)QCDTARO's. The
rotational symmetry is restored better as an action gets close to the
renormalized trajectory.


title: Precise Neutron Electric Form Factor from Lattice QCD

abstract:
  A new calculation of the neutron electric form factor is described.
Preliminary results for the connected part on a $20^{3}\times 32$ lattice are
presented. The methods for calculating the disconnected part are briefly
described.


title: Towards the glueball spectrum of full QCD

abstract:
  We present first results on masses of the scalar and tensor glueballs as well
as of the torelon from simulations of QCD with two light flavours of Wilson
fermions. The gauge configurations of extent 16^3*32 at beta = 5.6 and kappa =
0.156, 0.157 and 0.1575 have been generated as part of the SESAM collaboration
programme. The present lattice resolutions correspond to 1/a = 2.0-2.3 GeV and
ratios m(pi)/m(rho) = 0.83, 0.76 and 0.71, respectively. Studies on larger
lattice volumes and closer to the chiral limit are in progress.


title: Improved lattice actions

abstract:
  The main strategies to reduce lattice artifacts for spin models, gauge
fields, free fermions and QCD are discussed.


title: Phase transitions in quantum chromodynamics

abstract:
  The current understanding of finite temperature phase transitions in QCD is
reviewed. A critical discussion of refined phase transition criteria in
numerical lattice simulations and of analytical tools going beyond the
mean-field level in effective continuum models for QCD is presented.
Theoretical predictions about the order of the transitions are compared with
possible experimental manifestations in heavy-ion collisions. Various places in
phenomenological descriptions are pointed out, where more reliable data for
QCD's equation of state would help in selecting the most realistic scenario
among those proposed. Unanswered questions are raised about the relevance of
calculations which assume thermodynamic equilibrium. Promising new approaches
to implement nonequilibrium aspects in the thermodynamics of heavy-ion
collisions are described.


title: A Study of Finite Temperature Gauge Theory in (2+1) Dimensions

abstract:
  We determine the critical couplings and the critical exponents of the finite
temperature transition in SU(2) and SU(3) pure gauge theory in (2+1)
dimensions. We also measure Wilson loops at $T=0$ on a wide range of $\beta$
values using APE smearing to improve the signal. We extract the string tension
$\sigma$ from a fit to large distances, including a string fluctuation term.
With these two entities we calculate $T_c/\sqrt{\sigma}$.


title:
The Non-Perturbative ${\cal O}(g^6)$ Contribution to the Free Energy of
  Hot SU(N) Gauge Theory

abstract:
  The non-perturbative input necessary for the determination of the ${\cal
O}(g^6)$ part of the weak coupling expansion of the free energy density for
SU(2) and SU(3) gauge theories is estimated. Although the perturbative
information completing the contribution to this order is missing, we give
arguments that the magnetic fluctuations are dominated by screened elementary
magnetic gluons.


title: Glueballs on the three-sphere

abstract:
  We study the non-perturbative effects of the global features of the
configuration space for SU(2) gauge theory on the three-sphere. The strategy is
to reduce the full problem to an effective theory for the dynamics of the
low-energy modes. By explicitly integrating out the high-energy modes, the
one-loop correction to the effective hamiltonian is obtained. Imposing the
$\theta$ dependence through boundary conditions in configuration space
incorporates the non-perturbative effects of the non-contractable loops in the
full configuration space. After this we obtain the glueball spectrum of the
effective theory with a variational method.


title: Recent MILC spectrum results

abstract:
  We report on results from three spectrum calculations with staggered quarks:
1) a quenched calculation with the standard action for the gluons and quarks;
2) a quenched calculation with improved actions for both the gluons and quarks;
and 3) a calculation with two flavors of dynamical quarks using the standard
actions for the gluons and quarks.


title: Quenched Hadron Spectroscopy with Improved Actions

abstract:
  A variety of different combinations of improved gluon and fermion actions is
tested for quenched hadron spectroscopy


title: Super-heavy Quarkonia as a probe of the QCD Vacuum

abstract:
  We investigate the effect of a non-perturbative gluon condensate on the
spectrum of bound states of extremely heavy quarks using Non-Relativistic-QCD
(NRQCD). Simulations are done with an improved gluon action on small lattices.
We compare our numerical results with perturbative calculations to test the
consistency.


title: Progress report on hadron spectroscopy with improved actions

abstract:
  Quenched light hadron masses are measured on blocked lattices, using 6
different lattice discretizations of the Dirac operator. Results are compared
with those of unblocked lattices, allowing for a ``ranking'' of the Dirac
discretizations.


title:
Properties of the non-Gaussian fixed point in 4D compact U(1) lattice
  gauge theory

abstract:
  We examine selected properties of the gauge-ball spectrum and fermionic
variables in the vicinity of the recently discussed non-Gaussian fixed point of
4D compact U(1) lattice gauge theory within the quenched approximation.
Approaching the critical point from within the confinement phase, our data
support scaling of $T1^{+-}$ gauge-ball states in units of the string tension
square root. The analysis of the chiral condensate within the framework of a
scaling form for the equation of state suggests non mean-field values for the
magnetic exponents $\delta$ and $\beta_{exp}$.


title: QCD Spectrum --- 1996

abstract:
  Progress on the calculation of the spectrum from lattice calculations is
reviewed. Particular emphasis is placed on discussing our ability to control
possible systematic errors coming from finite volume, and extrapolations in
quark mass and lattice spacing. Recent approaches based on improved actions are
compared.


title: Non-perturbative renormalization in kaon decays

abstract:
  We discuss the application of the MPSTV non-perturbative method \cite{NPM} to
the operators relevant to kaon decays. This enables us to reappraise the
long-standing question of the $\Delta I=1/2$ rule, which involves
power-divergent subtractions that cannot be evaluated in perturbation theory.
We also study the mixing with dimension-six operators and discuss its
implications to the chiral behaviour of the $B_K$ parameter.


title:
Computing the lowest eigenvalues of the Fermion matrix by subspace
  iterations

abstract:
  Subspace iterations are used to minimise a generalised Ritz functional of a
large, sparse Hermitean matrix. In this way, the lowest $m$ eigenvalues are
determined. Tests with $1 \leq m \leq 32$ demonstrate that the computational
cost (no. of matrix multiplies) does not increase substantially with $m$. This
implies that, as compared to the case of a $m=1$, the additional eigenvalues
are obtained for free.


title: Quenched Chiral Logs, the $\eta'$ Mass, and the Hairpin Diagram

abstract:
  Limits on the size of quenched chiral logs in the pion mass for Wilson
fermions are investigated. The smallness of chiral logs is shown to be a result
of the suppression of the hairpin diagram for small $p^2$, such that the value
of the hairpin on the pion mass shell is much smaller than the physical
$m_{\eta'}^2$. A direct calculation of the topological susceptibility from the
same data gives $m_{\eta'}\approx 1$ GeV.


title: Why a Particle Physicist is Interested in DNA Branch Migration

abstract:
  We describe an explicitly discrete model of the process of DNA branch
migration. The model matches the existing data well, but we find that branch
migration along long strands of DNA ($N \simge 40$~bp) is also well modeled by
continuum diffusion. The discrete model is still useful for guiding future
experiments.


title: Gauge theories induced by bosons in fundamental representation

abstract:
  A lattice theory of scalar bosons in the fundamental representation of the
gauge group $SU(N_c)$ and of the global symmetry group $SU(N_f)$ is shown to
induce a standard gauge theory only at large $N_f$. The system is in a
deconfined phase at strong scalar self-coupling and any finite $N_f$. The
requirement of convergence of the effective gauge action imposes a lower limit
on the scalar mass.


title: Towards Highly Improved Quark Actions

abstract:
  We describe two ideas useful in the construction of highly improved quark
actions for simulations on coarse lattices:
  (1) Field transformations to solve the doubler problem without destroying
tree-level improvement for on- or off-shell quantities.
  (2) Anisotropic lattices with smaller temporal than spatial lattice spacing.
We present first simulation results for the quenched light hadron and
charmonium spectra obtained with a D234 action on anisotropic lattices.


title: Critical exponents in abelian projected $SU(2)$ QCD

abstract:
  The critical properties of the abelian Polyakov loop and the Polyakov loop in
terms of Dirac string are studied in finite temperature abelian projected
$SU(2)$ QCD. The critical point and the critical exponents are determined from
each Polyakov loop in the maximally abelian gauge using the finite-size scaling
analyses. Those critical points and exponents are in good agreement with those
from non-abelian Polyakov loops.