title:
Absence of Parity-Flavor Breaking Phase in QCD with two Flavors of
  Wilson fermions for beta greater than or equal to 5.0

abstract:
  We present data testing the existence of a parity-flavor breaking phase in
simulations of QCD with two flavors of light Wilson fermions. This is done by
explicit simulations on lattice sizes of $6^4$, $8^4$ and $10^4$ for a variety
of values of $\beta$ and $\kappa$ as well as the coefficient, $h$, of an
explicit breaking term included in the action. We find that at $\beta=6/g^2 $
equal to or greater than 5.0 extrapolation in the parameter $h$ as well as in
the lattice volume show no indication of a phase where parity and flavor are
spontaneously broken in the limit of zero $h$.


title: $B$ Spectroscopy from NRQCD with Dynamical Fermions

abstract:
  We present a lattice investigation, partially including the effects of
dynamical quarks, of the heavy-light mesons using NRQCD for the heavy quark and
the Wilson action for the light quark. We performed an extensive calculation of
the spectrum employing a multi-state, multi-exponential fitting analysis which
enabled us to extract the $2S{-}1S$ splitting as well as the $^1P_1{-}\bar{S}$
and hyperfine splittings. The Wilson action introduces a large systematic error
into the calculation, and within this uncertainty we obtain agreement with
experiment. We performed a comprehensive calculation of the heavy-light meson
mass, investigating three methods and their range of validity. The agreement
found between these methods confirms that Lorentz invariance can be restored at
this order in NRQCD by a constant shift to all masses. We calculated
spectroscopic quantities over a wide range in heavy quark mass and were able to
perform a detailed investigation of heavy quark symmetry around the $b$ quark
mass. In particular, we extracted the nonperturbative coefficients of terms in
the heavy quark expansion of the meson binding energy. We demonstrate the
importance of using tadpole-improved operators in such a calculation.


title:
Lattice Operators for Moments of the Structure Functions and their
  Transformation under the Hypercubic Group

abstract:
  For lattice operators that are relevant to the calculation of moments of
nucleon structure functions we investigate the transformation properties under
the hypercubic group. We give explicit bases of irreducible subspaces for
tensors of rank up to 4.


title: Chiral Anomaly on a Lattice

abstract:
  A calculation of the chiral anomaly on a finite lattice without fermion
doubling is presented . The lattice gauge field is defined in the spirit of
noncommutative geometry. Standard formulas for the continuum anomaly are
obtained as a limit.


title:
Light hadron masses with a tadpole-improved next-nearest-neighbour
  lattice fermion action

abstract:
  Calculations of hadron masses are done in quenched approximation using gauge
field and fermion actions which are both corrected for discretization errors to
$O(a^2)$ at the classical level and which contain tadpole improvement factors.
The fermion action has both nearest-neighbour and next-nearest-neighbour
couplings in the kinetic and Wilson terms. Simulations done at lattice spacings
of $0.27$ and $0.4$fm yield hadron masses which are already quite close to
experimental values. The results are compared to Wilson action calculations
done at comparable lattice spacings.


title:
A strong-coupling analysis of two-dimensional O(N) sigma models with
  N<=2 on square, triangular and honeycomb lattices

abstract:
  The critical behavior of two-dimensional ${\rm O}(N)$ $\sigma$ models with
$N\leq 2$ on the square, triangular, and honeycomb lattices is investigated by
an analysis of the strong-coupling expansion of the two-point fundamental
Green's function $G(x)$, calculated up to 21st order on the square lattice,
15th order on the triangular lattice, and 30th order on the honeycomb lattice.
For $N<2$ the critical behavior is of power-law type, and the exponents
$\gamma$ and $\nu$ extracted from our strong-coupling analysis confirm exact
results derived assuming universality with solvable solid-on-solid models. At
$N=2$, i.e., for the 2-$d$ XY model, the results from all lattices considered
are consistent with the Kosterlitz-Thouless exponential approach to
criticality, characterized by an exponent $\sigma=1/2$, and with universality.
The value $\sigma=1/2$ is confirmed within an uncertainty of few per cent. The
prediction $\eta=1/4$ is also roughly verified. For various values of $N\leq
2$, we determine some ratios of amplitudes concerning the two-point function
$G(x)$ in the critical limit of the symmetric phase. This analysis shows that
the low-momentum behavior of $G(x)$ in the critical region is essentially
Gaussian at all values of $N\leq 2$. New exact results for the long-distance
behavior of $G(x)$ when $N=1$ (Ising model in the strong-coupling phase)
confirm this statement.


title:
A Study of the Bulk Phase Transitions of the SU(2) Lattice Gauge Theory
  with Mixed Action

abstract:
  Using the finite size scaling theory, we re-examine the nature of the bulk
phase transition in the fundamental-adjoint coupling plane of the SU(2) lattice
gauge theory at $\beta_A = 1.25$ where previous finite size scaling
investigations of the deconfinement phase transition showed it to be of first
order for temporal lattices with four sites. Our simulations on $N^4$ lattices
with N=6, 8, 10, 12 and 16 show an absence of a first order bulk phase
transition. We find the discontinuity in the average plaquette to decrease
approximately linearly with $N$. Correspondingly, the plaquette susceptibility
grows a lot slower with the 4-volume of the lattice than expected from a first
order bulk phase transition.


title: Gauge Boson Masses in the 3-d, SU(2) Gauge-Higgs Model

abstract:
  We study gauge boson propagators in the symmetric and symmetry broken phases
of the 3-d, $SU(2)$ gauge-Higgs model. Correlation functions for the gauge
fields are calculated in Landau gauge. They are found to decay exponentially at
large distances leading to a non-vanishing mass for the gauge bosons. We find
that the W-boson screening mass drops in the symmetry broken phase when
approaching the critical temperature. In the symmetric phase the screening mass
stays small and is independent of the scalar--gauge coupling (the hopping
parameter). Numerical results coincide with corresponding calculations
performed for the pure gauge theory. We find $m_w = 0.35(1)g^2T $ in this phase
which is consistent with analytic calculations based on gap equations. This is,
however, significantly smaller than masses extracted from gauge invariant
vector boson correlation functions. As internal consistency check we also have
calculated correlation functions for gauge invariant operators leading to
scalar and vector boson masses. Finite lattice size effects have been
systematically analyzed on lattices of size $L^2\times L_z$ with $L=4-24$ and
$L_z = 16 - 128$.


title:
The Role of Vortex Strings in the Non-Compact Lattice Abelian Higgs
  Model

abstract:
  The non-compact lattice version of the Abelian Higgs model is studied in
terms of its topological excitations. The Villain form of the partition
function is represented as a sum over world-sheets of gauge-invariant
``vortex'' strings. The phase transition of the system is then related to the
density of these excitations. Through Monte Carlo simulations the density of
the vortex sheets is shown to be a good order parameter for the system. The
vortex density essentially vanishes in the Higgs phase, and the Coulomb phase
consists of a single vortex condensate.


title: Perturbative Renormalization of Lattice Bilinear Quark Operators

abstract:
  Our aim is to compute the lower moments of the unpolarized and polarized
deep-inelastic structure functions of the nucleon on the lattice. The
theoretical basis of the calculation is the operator product expansion. To
construct operators with the appropriate continuum behavior out of the bare
lattice operators one must absorb the effects of momentum scales far greater
than any physical scale into a renormalization of the operators. In this work
we compute the renormalization constants of all bilinear quark operators of
leading twist and spin up to four. The calculation is done for Wilson fermions
and in the quenched approximation where dynamical quark loops are neglected.


title: The Emergence of a Heavy Quark Family on a Lattice

abstract:
  Within the framework of the ``Rome approach'' for a lattice chiral gauge
theory, the four-quark interaction with flavour symmetry is included. We
analyse spontaneous symmetry breaking and compute composite modes and their
contributions to the ground state energy. As a result, it is shown that the
emergence of a heavy quark family is the energetically favoured solution.


title:
Implementation of Symanzik's Improvement Program for Simulations of
  Dynamical Wilson Fermions in Lattice QCD

abstract:
  We discuss the implementation of a Sheikholeslami-Wohlert term for
simulations of lattice QCD with dynamical Wilson fermions as required by
Symanzik's improvement program. We show that for the Hybrid Monte Carlo or
Kramers equation algorithm standard even-odd preconditioning can be maintained.
We design tests of the implementation using analytically and numerically
computed cumulant expansions. We find that, for situations where the average
number of Conjugate Gradient iterations exceeds 200, the overhead is only about
20%.


title:
Magnetic Monopoles and the Dual London Equation in SU(3) Lattice Gauge
  Theory

abstract:
  We propose a method for the determination of magnetic monopole currents in
non-Abelian gauge theories which does not need a projection to Abelian degrees
of freedom. With this definition we are able to determine the distribution of
magnetic currents and electric fields for the gluonic flux tube between a pair
of static charges. Further we check the validity of the Gauss law and the dual
London equation in a gauge invariant formulation.


title:
Lattice Fermions Coupled to Interpolated Gauge Fields - Results in 2
  Dimensions

abstract:
  We discuss a new approach for putting gauge theories on the lattice. The
gauge fields are defined on the lattice only, but are interpolated to the
interior of the lattice cells, where they couple to continuum fermions. The
purpose of this approach is to avoid doublers and keep the chiral symmetry of
the action intact. In two dimensional models (Schwinger model and chiral
Schwinger model) many results for this hybrid approach can be obtained
analytically. For the vectorlike Schwinger model we concentrate on proving the
existence of a critical point where the continuum limit can be constructed, on
analyzing the chiral properties and on proving the Osterwalder-Schrader
positivity which allows the reconstruction of the physical Hilbert space. We
conclude with outlining how the results can be generalized to the chiral
Schwinger model.


title: Exact Local Bosonic Algorithm for Full QCD

abstract:
  We present an exact local bosonic algorithm for the simulation of dynamical
fermions in lattice QCD. It is based on a non-hermitian polynomial
approximation of the inverse of the quark matrix and a global Metropolis
accept/reject correction of the systematic errors. We show that this algorithm
is a real alternative to the Hybrid Monte Carlo algorithm.


title:
Dual Superconductor Scenario of Confinement: A Systematic Study of
  Gribov Copy Effects

abstract:
  We perform a study of the effects from maximal abelian gauge Gribov copies in
the context of the dual superconductor scenario of confinement, on the basis of
a novel approach for estimation of systematic uncertainties from incomplete
gauge fixing. We present numerical results, in SU(2) lattice gauge theory,
using the overrelaxed simulated annealing gauge fixing algorithm. We find
abelian and non-abelian string tensions to differ significantly, their ratio
being 0.92(4) at BETA = 2.5115. An approximate factorization of the abelian
potential into monopole and photon contributions has been confirmed, the former
giving rise to the abelian string tension.


title: 2D Quantum Gravity -Three States of Surfaces-

abstract:
  Two-dimensional random surfaces are studied numerically by the dynamical
triangulation method. In order to generate various kinds of random surfaces,
two higher derivative terms are added to the action. The phases of surfaces in
the two-dimensional parameter space are classified into three states: flat,
crumpled surface, and branched polymer. In addition, there exists a special
point (pure gravity) corresponding to the universal fractal surface. A new
probe to detect branched polymers is proposed, which makes use of the
minbu(minimum neck baby universe) analysis. This method can clearly distinguish
the branched polymer phase from another according to the sizes and arrangements
of baby universes. The size distribution of baby universes changes drastically
at the transition point between the branched polymer and other kind of surface.
The phases of surfaces coupled with multi-Ising spins are studied in a similar
manner.


title: Simple ansatz for the lattice fermion determinant

abstract:
  An ansatz for the fermion vacuum functional on a lattice is proposed. It is
proved to reproduce correct continuum limit for convergent diagrams of any
finite order in smooth external fields, as well as consistent chiral anomalies,
and ensures gauge invariance of the absolute value of the functional at any
lattice spacing. The ansatz corresponds to a certain non-local fermion action
having global chiral invariance. Problems caused by non-smooth gauge fields are
discussed.


title: Instantons and Fixed Point Actions in SU(2) Gauge Theory

abstract:
  We describe the properties of instantons in lattice gauge theory when the
action is a fixed point action of some renormalization group transformation. We
present a theoretically consistent method for measuring topological charge
using an inverse renormalization group transformation. We show that, using a
fixed point action, the action of smooth configurations with non-zero
topological charge is greater than or equal to its continuum value
$8\pi^2/g^2$.


title:
CORE Technology and Exact Hamiltonian Real-Space Renormalization Group
  Transformations

abstract:
  The COntractor REnormalization group (CORE) method, a new approach to solving
Hamiltonian lattice systems, is presented. The method defines a systematic and
nonperturbative means of implementing Kadanoff-Wilson real-space
renormalization group transformations using cluster expansion and contraction
techniques. We illustrate the approach and demonstrate its effectiveness using
scalar field theory, the Heisenberg antiferromagnetic chain, and the
anisotropic Ising chain. Future applications to the Hubbard and t-J models and
lattice gauge theory are discussed.


title: Field strength correlations in the QCD vacuum at short distance

abstract:
  We determine by numerical simulations on a lattice the gauge--invariant
two--point correlation function of the gauge field strengths in the QCD vacuum,
down to a distance of 0.1 fm.


title: Gauge--invariant field correlators in QCD at finite temperature

abstract:
  We study by numerical simulations on a lattice the behaviour of the
gauge--invariant two--point correlation functions of the gauge field strengths
across the deconfinement phase transition.


title: Finite Volume Effects and Quenched Chiral Logarithms

abstract:
  We have measured the valence pion mass and the valence chiral condensate on
lattice configurations generated with and without dynamical fermions. We find
that our data and that of others is well represented by a linear relationship
between $m_{\pi}^2$ and the valence quark mass, with a non-zero intercept. For
our data, we relate the intercept to finite volume effects visible in the
valence chiral condensate. We see no evidence for the singular behavior
expected from quenched chiral logarithms.


title:
Pseudofermion observables for static heavy meson decay constants on the
  lattice

abstract:
  A method based on the Monte Carlo inversion of the Dirac operator on the
lattice provides low noise results for the correlations entering the definition
of the heavy meson decay constant in the static limit. The method is
complementary to the usual method of smeared sources, avoids the systematic
error arising from optimizing the size of the smearing volume and is more
efficient for the values of lattice parameters that we have explored.


title: Molecular dynamics for full QCD simulations with an improved action

abstract:
  I derive the equation of motion in molecular dynamics for doing full lattice
QCD simulations with clover quarks. The even-odd preconditioning technique,
expected to significantly reduce the computational effort, is further developed
for the simulations.


title:
SO(3) vortices as a mechanism for generating a mass gap in the 2d SU(2)
  principal chiral model

abstract:
  We propose a mechanism that can create a mass gap in the SU(2) chiral spin
model at arbitrarily small temperatures. We give a sufficient condition for the
mass gap to be non-zero in terms of the behaviour of an external Z(2) flux
introduced by twisted boundary conditions. This condition in turn is
transformed into an effective dual Ising model with an external magnetic field
generated by SO(3) vortices. We show that having a nonzero magnetic field in
the effective Ising model is sufficient for the SU(2) system to have a mass
gap. We also show that certain vortex correlation inequalities, if satisfied,
would imply a nonzero effective magnetic field. Finally we give some
plausibility arguments and Monte Carlo evidence for the required correlation
inequalities.


title: The SU(2)-Higgs model on asymmetric lattices

abstract:
  We calculate the ${\cal O}(g^2,\lambda)$ corrections to the coupling
anisotropies of the SU(2)-Higgs model on lattices with asymmetric lattice
spacings. These corrections are obtained by a one-loop calculation requiring
the rotational invariance of the gauge- and Higgs-boson propagators in the
continuum limit.


title:
Further evidence that the transition of 4D dynamical triangulation is
  1st order

abstract:
  We confirm recent claims that, contrary to what was generally believed, the
phase transition of the dynamical triangulation model of four-dimensional
quantum gravity is of first order. We have looked at this at a volume of 64,000
four-simplices, where the evidence in the form of a double peak histogram of
the action is quite clear.


title: Perturbative study for domain-wall fermions in 4+1 dimensions

abstract:
  We investigate a U(1) chiral gauge model in 4+1 dimensions formulated on the
lattice via the domain-wall method. We calculate an effective action for smooth
background gauge fields at a fermion one loop level. From this calculation we
discuss properties of the resulting 4 dimensional theory, such as gauge
invariance of 2 point functions, gauge anomalies and an anomaly in the fermion
number current.


title: The Coupled Cluster Method in Hamiltonian Lattice Field Theory

abstract:
  The coupled cluster or exp S form of the eigenvalue problem for lattice
Hamiltonian QCD (without quarks) is investigated. A new construction
prescription is given for the calculation of the relevant coupled cluster
matrix elements with respect to an orthogonal and independent loop space basis.
The method avoids the explicit introduction of gauge group coupling
coefficients by mapping the eigenvalue problem onto a suitable set of character
functions, which allows a simplified procedure. Using appropriate group
theoretical methods, we show that it is possible to set up the eigenvalue
problem for eigenstates having arbitrary lattice momentum and lattice angular
momentum.


title:
Two-dimensional model of dynamical fermion mass generation in strongly
  coupled gauge theories

abstract:
  We generalize the $N_F=2$ Schwinger model on the lattice by adding a charged
scalar field. In this so-called $\chi U\phi_2$ model the scalar field shields
the fermion charge, and a neutral fermion, acquiring mass dynamically, is
present in the spectrum. We study numerically the mass of this fermion at
various large fixed values of the gauge coupling by varying the effective
four-fermion coupling, and find an indication that its scaling behavior is the
same as that of the fermion mass in the chiral Gross-Neveu model. This suggests
that the $\chi U\phi_2$ model is in the same universality class as the
Gross-Neveu model, and thus renormalizable and asymptotic free at arbitrary
strong gauge coupling.


title: Lattice Regularization of the Chiral Schwinger Model

abstract:
  We analyze the chiral Schwinger model on an infinite lattice using the
continuum definition of the fermion determinant and a linear interpolation of
the lattice gauge fields. For non-compact and Wilson formulation of the gauge
field action it is proven that the effective lattice model is
Osterwalder-Schrader positive, which is a sufficient condition for the
reconstruction of a physical Hilbert space from the model defined on a
Euclidean lattice. For the non-compact model we furthermore establish the
existence of critical points where the corresponding continuum theory can be
reconstructed. We show that the continuum limit for the two-point functions of
field strength and chiral densities can be controlled analytically. The article
ends with some remarks on fermionic observables.


title:
Random matrix model of QCD at finite density and the nature of the
  quenched limit

abstract:
  We use a random matrix model to study chiral symmetry breaking in QCD at
finite chemical potential $\mu$. We solve the model and compute the eigenvalue
density of the Dirac matrix on a complex plane. A naive ``replica trick'' fails
for $\mu\neq0$: we find that quenched QCD is not a simple $n\to0$ limit of QCD
with $n$ quarks. It is the limit of a theory with $2n$ quarks: $n$ quarks with
original action and $n$ quarks with conjugate action. The results agree with
earlier studies of lattice QCD at $\mu\neq0$ and provide a simple analytical
explanation of a long-standing puzzle.


title: Massive Fermions in Lattice Gauge Theory

abstract:
  This paper presents a formulation of lattice fermions applicable to all quark
masses, large and small. We incorporate interactions from previous
light-fermion and heavy-fermion methods, and thus ensure a smooth connection to
these limiting cases. The couplings in improved actions are evaluated for
arbitrary fermion mass~$m_q$, without expansions around small- or large-mass
limits. We treat both the action and external currents. By interpreting
on-shell improvement criteria through the lattice theory's Hamiltonian, one
finds that cutoff artifacts factorize into the form
$b_n(m_qa)[\vek{p}a]^{s_n}$, where $\vek{p}$ is a momentum characteristic of
the system under study, $s_n$ is related to the dimension of the $n$th
interaction, and $b_n(m_qa)$ is a bounded function, numerically
always~$\order(1)$ or less. In heavy-quark systems $\vek{p}$ is typically
rather smaller than the fermion mass~$m_q$. Therefore, artifacts of order
$(m_qa)^s$ do not arise, even when $m_qa\gsim1$. An important by-product of our
analysis is an interpretation of the Wilson and Sheikholeslami-Wohlert actions
applied to nonrelativistic fermions.


title: A lattice fermion without doubling

abstract:
  A free fermion without doubler is formulated on 1+D dimensional discrete
Minkowski space-time. The action is not hermitian but causes no harm. In 1+3
dimensional massless case the equation describes a single species of Dirac
particle in the continuous space-time limit. In 1+1 dimensional massless case
the equation is the same as the automaton equation by 't Hooft and describes a
chiral fermion. The time evolution operator is unitary and the norm is
conserved. For interacting fermions with gauge fields the evolution operator is
not unitary. If it is considered as an approximation for the theory on
continuous space-time, the path integral formalism can be applied, where the
fermion without doubling is used. Consequences of loosening the unitarity
condition on the time evolution operator is discussed.


title: Critical Phenomena with Linked Cluster Expansions in a Finite Volume

abstract:
  Linked cluster expansions are generalized from an infinite to a finite
volume. They are performed to 20th order in the expansion parameter to approach
the critical region from the symmetric phase. A new criterion is proposed to
distinguish 1st from 2nd order transitions within a finite size scaling
analysis. The criterion applies also to other methods for investigating the
phase structure such as Monte Carlo simulations. Our computational tools are
illustrated at the example of scalar O(N) models with four and six-point
couplings for $N=1$ and $N=4$ in three dimensions. It is shown how to localize
the tricritical line in these models. We indicate some further applications of
our methods to the electroweak transition as well as to models for
superconductivity.


title:
Finite Temperature Properties of SO(3) Lattice Gauge Theories and their
  implications for the continuum limit

abstract:
  It is shown that $SO(3)$ lattice gauge theory on finite size lattices has
metastable states related to the ground states of both the bulk transition and
the finite temperature transition. The Polyakov line variable in the adjoint
representation of $SU(2)$ is used to trace the origin of these metastable
states. It is also argued that a second order finite temperature transition in
the continuum theory is not inconsistent with the first order transition in
$SO(3)$ lattice gauge theory and the absence of a $Z(2)$ global symmetry.


title: Physical and unphysical effects in the mixed SU(2)/SO(3) gauge theory

abstract:
  We investigate possible problems with universality in lattice gauge theory
where a mixed fundamental SU(2) and SO(3)-invariant gauge group is used: the
(second order) finite temperature phase transition becomes involved with first
order effects with increased SO(3) coupling, and this first order effect has a
noticeable coupling dependence for small lattices. We produce evidence that the
first order transition is essentially bulk in nature as generally believed, and
that the finite temperature effects start to separate out from the lower end of
the bulk effects for a lattice of 8 sites in the finite temperature direction.
We strengthen our picture of the first order effects as artefacts by using an
improved action: this shifts the end point of the first order line away from
the fundamental SU(2) axis.


title: A New Lattice Action for Studying Topological Charge

abstract:
  We propose a new lattice action for non-abelian gauge theories, which will
reduce short-range lattice artifacts in the computation of the topological
susceptibility. The standard Wilson action is replaced by the Wilson action of
a gauge covariant interpolation of the original fields to a finer lattice. If
the latter is fine enough, the action of all configurations with non-zero
topological charge will satisfy the continuum bound. As a simpler example we
consider the $O(3)$ $\sigma$-model in two dimensions, where a numerical
analysis of discretized continuum instantons indicates that a finer lattice
with half the lattice spacing of the original is enough to satisfy the
continuum bound.


title: A Convergence Proof for Linked Cluster Expansions

abstract:
  We prove that for a general $N$-component model on a $d$-dimensional lattice
$\bZ^d$ with pairwise nearest-neighbor coupling and general local interaction
obeying a stability bound the linked cluster expansion has a finite radius of
convergence. The proof uses Mayer Montroll equations for connected Green
functions.


title:
Comparison of 4d and 3d Lattice Results for the Electroweak Phase
  Transition

abstract:
  We compare 4d lattice results for the finite temperature phase transition in
the SU(2)+Higgs model with 3d lattice results for the phase transition in the
corresponding dimensionally reduced effective theory. While the large errorbars
and the lack of a relation of the 4d lattice gauge coupling to continuum
physics prevent rigorous conclusions, the results are nevertheless compatible.
This provides a direct non-perturbative check of dimensional reduction in the
present context.


title: Lattice Gauge Fields and Noncommutative Geometry

abstract:
  Conventional approaches to lattice gauge theories do not properly consider
the topology of spacetime or of its fields. In this paper, we develop a
formulation which tries to remedy this defect. It starts from a cubical
decomposition of the supporting manifold (compactified spacetime or spatial
slice) interpreting it as a finite topological approximation in the sense of
Sorkin. This finite space is entirely described by the algebra of cochains with
the cup product. The methods of Connes and Lott are then used to develop gauge
theories on this algebra and to derive Wilson's actions for the gauge and Dirac
fields therefrom which can now be given geometrical meaning. We also describe
very natural candidates for the QCD theta term and Chern-Simons action
suggested by this algebraic formulation. Some of these formulations are simpler
than currently available alternatives. The paper treats both the functional
integral and Hamiltonian approaches.


title: Phase Transition in Lattice Surface Systems with Gonihedric Action

abstract:
  We prove the existence of an ordered low temperature phase in a model of
soft-self-avoiding closed random surfaces on a cubic lattice by a suitable
extension of Peierls contour method. The statistical weight of each surface
configuration depends only on the mean extrinsic curvature and on an
interaction term arising when two surfaces touch each other along some contour.
The model was introduced by F.J. Wegner and G.K. Savvidy as a lattice version
of the gonihedric string, which is an action for triangulated random surfaces.


title: First Evidence of $N_f$-Dependence in the QCD Interquark Potential

abstract:
  We present a lattice calculation of the interquark potential between static
quarks in a ``full'' QCD simulation with 2 flavours of dynamical Wilson-quarks
at three intermediate sea-quark masses. We work at $\beta = 5.6$ on lattice
size of $16^3 \times 32$ with 100 configurations per sea-quark mass. We compare
the full QCD potential with its quenched counterpart at equal lattice spacing,
$a^{-1} \simeq 2.0$ GeV, which is at the onset of the quenched scaling regime.
We find that the full QCD potential lies consistently below that of quenched
QCD. We see no evidence for string-breaking effects on these lattice volumes,
$V \simeq (1.5\,\,{\rm fm})^3$.


title:
Multi-Grid Monte Carlo via $XY$ Embedding I. General Theory and
  Two-Dimensional $O(N)$-Symmetric Nonlinear $\sigma$-Models

abstract:
  We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on
the embedding of an $XY$ model into the target model, and we study its
mathematical properties for a variety of nonlinear $\sigma$-models. We then
apply the method to the two-dimensional $O(N)$-symmetric nonlinear
$\sigma$-models (also called $N$-vector models) with $N=3,4,8$ and study its
dynamic critical behavior. Using lattices up to $256 \times 256$, we find
dynamic critical exponents $z_{int,{\cal M}^2} \approx 0.70 \pm 0.08$, $0.60
\pm 0.07$, $0.52 \pm 0.10$ for $N=3,4,8$, respectively (subjective 68\%
confidence intervals). Thus, for these asymptotically free models, critical
slowing-down is greatly reduced compared to local algorithms, but not
completely eliminated; and the dynamic critical exponent does apparently vary
with $N$. We also analyze the static data for $N=8$ using a finite-size-scaling
extrapolation method. The correlation length $\xi$ agrees with the four-loop
asymptotic-freedom prediction to within $\approx 1\%$ over the interval $12 <
\xi < 650$.


title: Some aspects of simulation algorithms for dynamical fermions

abstract:
  Three topics concerning fermion simulation algorithms are discussed: 1.) A
performance comparison of the multiboson technique to simulate dynamical
fermions and the Kramers equation algorithm, 2.) the question of reversibility
in the Hybrid Monte Carlo algorithm and 3.) the implementation of Symanzik's
improvement program for dynamical Wilson fermions.


title: One-loop effective action for SU(2) gauge theory on S^3

abstract:
  We consider the effective theory for the low-energy modes of SU(2) gauge
theory on the three-sphere. By explicitely integrating out the high-energy
modes, the one-loop correction to the hamiltonian for this problem is obtained.
We calculate the influence of this correction on the glueball spectrum.


title:
Scaling and Topological Charge of a Fixed Point Action for $SU(2)$ Gauge
  Theory

abstract:
  We construct a few parameter approximate fixed point action for SU(2) pure
gauge theory and subject it to scaling tests, via Monte Carlo simulation. We
measure the critical coupling for deconfinement for lattices of temporal extent
$N_t=2$, 3, 4, the torelon mass at fixed physical volume, and the string
tension (and heavy quark potential) from Wilson loops. We calculate the
topological susceptibility using inverse blocking and show that it scales over
the observed range of lattice spacings.


title: Strings in Computer

abstract:
  Complex structures are determined for surfaces with $S^2$ and $T^2$
topologies generated by the dynamical triangulation method. For a surface with
$S^2$ topology the spacial distribution of the conformal mode is obtained,
while for the case of $T^2$ topology the distribution of the moduli parameter
is calculated. It is also shown that the network of Feynman diagrams of massive
$\phi^3$ scalar theory has a unique complex structure. This gives a numerical
justification of the hadronic string model for explaining the n-particle dual
amplitude.


title: Deconfinement in QCD with dynamical quarks

abstract:
  We study the phase structure of full QCD within the canonical ensemble with
respect to triality in a lattice formulation. The procedure for the calculation
of the effective potentials in this case is given. As an example we consider
the three dimensional SU(2) gauge model at finite temperatures in the strong
coupling region. The potential exhibits a deconfinement phase transition unlike
the similar potential obtained in the grand canonical ensemble which
demonstrates explicit Z(N) symmetry breaking at any temperature. Furthermore,
we investigate the effective potential with the chiral condensate included. In
contradiction to other authors, we find chiral symmetry restoration in all
triality sectors. In the scheme with massless staggered fermions we observe
chiral symmetry restoration accompanying a deconfinement phase transition of
first order. Above the critical point, besides two Z(2) symmetric "deconfining"
vacua there exists a metastable "confining" vacuum in a wide region of
parameters. Such a picture could be interpreted as an indication on a mixed
state of hadrons and quarks in the vicinity of the critical line.


title:
Linked cluster expansions beyond nearest neighbour interactions:
  convergence and graph classes

abstract:
  We generalize the technique of linked cluster expansions on hypercubic
lattices to actions that couple fields at lattice sites which are not nearest
neighbours. We show that in this case the graphical expansion can be arranged
in such a way that the classes of graphs to be considered are identical to
those of the pure nearest neighbour interaction. The only change then concerns
the computation of lattice imbedding numbers. All the complications that arise
can be reduced to a generalization of the notion of free random walks,
including hopping beyond nearest neighbour. Explicit expressions for
combinatorical numbers of the latter are given. We show that under some general
conditions the linked cluster expansion series have a non-vanishing radius of
convergence.


title:
Optimized $\delta $ - Expansion for Lattice U(1) and SU(2) with
  Interpolating Continuum Action

abstract:
  Embedding the lattice gauge theory into a continuum theory allows to use the
continuum action as trial action in the variational calculation. Only
originally divergent graphs contribute. This leads to a very simple scheme
which makes it possible to write down explicit expressions for the plaquette
energy $E$ for U(1) in arbitrary space time dimension for the first three
orders of the expansion. For dimensions three and four one can even go up to
fourth order. This allows a rather thorough empirical investigation of the
convergence properties of the $\delta $-expansion, in particular near the phase
transition or the transition region, respectively. As already found in previous
work, the principle of minimal sensitivity can be only applied for $\beta $
above a certain value, because otherwise no extremum with respect to the
variational parameter exists. One can, however, extend the range of
applicability down to small $\beta $, by calculating instead of $E$ some power
$E^\kappa $, or by performing an appropriate Pad\'e transformation. We find
excellent agreement with the data for $\beta $ above the transition region for
the second and higher orders. Below the transition region the agreement is
rather poor in low orders, but quite impressive in fourth order. For SU(2) we
performed the calculation up to second order. The agreement with the data is
somewhat worse than in the abelian case.


title: Gravitational binding in 4D dynamical triangulation

abstract:
  In the dynamical triangulation model of four dimensional euclidean quantum
gravity we investigate gravitational binding. Two scalar test particles
(quenched approximation) have a positive binding energy, thereby showing that
the model can represent gravitational attraction.


title:
The exact equivalence of the two-flavour strong coupling lattice
  Schwinger model with Wilson fermions to a vertex model

abstract:
  In this paper a method previously employed by Salmhofer to establish an exact
equivalence of the one-flavour strong coupling lattice Schwinger model with
Wilson fermions to some 8-vertex model is applied to the case with two
flavours. As this method is fairly general and can be applied to strong
coupling QED and purely fermionic models with any (sufficiently small) number
of Wilson fermions in any dimension the purpose of the present study is mainly
a methodical one in order to gain some further experience with it. In the paper
the vertex model equivalent to the two-flavour strong coupling lattice
Schwinger model with Wilson fermions is found. It turns out to be some modified
3-state 20-vertex model on the square lattice, which can also be understood as
a regular 6-state vertex model. In analogy with the one- flavour case, this
model can be viewed as some loop model.


title: Improvement of the Staggered Fermion Operators

abstract:
  We present a complete and detailed derivation of the finite lattice spacing
corrections to staggered fermion matrix elements. Expanding upon arguments of
Sharpe, we explicitly implement the Symanzik improvement program demonstrating
the absence of order $a$ terms in the Symanzik improved action. We propose a
general program to improve fermion operators to remove $O(a)$ corrections from
their matrix elements, and demonstrate this program for the examples of matrix
elements of fermion bilinears and $B_K$. We find the former does have $O(a)$
corrections while the latter does not.


title: Improved Hamiltonian for Minkowski Yang-Mills Theory

abstract:
  I develop an improved Hamiltonian for classical, Minkowski Yang-Mills theory,
which evolves infrared fields with corrections from lattice spacing $a$
beginning at $O(a^4)$. I use it to investigate the response of Chern-Simons
number to a chemical potential, and to compute the maximal Lyapunov exponent.
Both quantities have small $a$ limits, in both cases within $10\% $ of the
limit found using the unimproved (Kogut Susskind) Hamiltonian. For the maximal
Lyapunov exponent the limits differ by about $5 \% $, significant at about $5
\sigma$, indicating that while a small $a$ limit exists, its value is corrupted
by lattice artefacts. For the response of Chern-Simons number the statistics
are not good enough to resolve $ 5 \% $ differences, but it seems possible in
analogy with the Lyapunov exponent that the final answer depends on the lattice
regulation.


title:
Dynamical flavour dependence of static heavy meson decay constants on
  the lattice

abstract:
  We study the dynamical flavour dependence of the lattice estimates of the
heavy meson decay constant in the static limit. We perform the analysis by
considering negative flavour numbers and by extrapolating the results to
positive values. We observe a sizeable flavour dependence which increases the
quenched estimates.


title: A Lattice Chiral Theory with Multifermion Couplings

abstract:
  Analyzing an $SU_L(2)\otimes U_R(1)$ chiral theory with multifermion
couplings on a lattice, we find a possible region in the phase space of
multifermion couplings, where no spontaneous symmetry breaking occurs, doublers
are decoupled as massive Dirac fermions consistently with the $SU_L(2)\otimes
U_R(1)$ chiral symmetry, the ``spectator'' fermion $\psi_R(x)$ is free mode,
whereas the normal mode of $\psi^i_L(x)$ is plausibly speculated to be chiral
in the continuum limit. This is not in agreement with the general belief of the
definite failure of theories so constructed.


title: SU(3) Thermodynamics on Small Lattices

abstract:
  The free energy density of the SU(3) gauge theory at temperatures T/T_c =
4/3, 3/2 and 2 is calculated on lattices with temporal extent as small as N_t =
2, 3 and spatial extent N_s = 4 N_t using parametrized fixed point actions.
Although cut-off effects are seen, they are hugely suppressed with respect to
Wilson and Symanzik-improved actions and at N_t = 3 there is already a good
agreement with the continuum limit as extrapolated from the results with the
Wilson action at N_t = 6 and 8.


title: A possible scaling region of chiral fermions on a lattice

abstract:
  We present the details of analyzing an $SU_L(2)\otimes U_R(1)$ chiral theory
with multifermion couplings on a lattice. An existence of a possible scaling
region in the phase space of multifermion couplings for defining the continuum
limit of chiral fermions is advocated. In this scaling region, no spontaneous
symmetry breaking occurs; the ``spectator'' fermion $\psi_R(x)$ is a free mode
and decoupled; doublers are decoupled as massive Dirac fermions consistently
with the $SU_L(2)\otimes U_R(1)$ chiral symmetry, whereas the normal mode of
$\psi_L^i(x)$ is plausibly speculated to be chiral in the continuum limit. This
is not in agreement with the general belief of the definite failure of theories
so constructed.


title: Improved Algorithm for Bosonized Fermion Determinant

abstract:
  Following the line of \cite{AS} we propose an improved algorithm which allows
to calculate a D-dimensional fermion determinant integrating the exponent of
D+1 dimensional Hermitean bosonic action. For a finite extra dimension the
corrections decrease exponentially.


title:
A new approach to significantly reduce the negative sign problem in
  quantum Monte Carlo

abstract:
  We present a new approach for Monte Carlo simulations of lattice quantum spin
systems which is able to eliminate the negative sign problem. Its complexity is
linear in the volume of the lattice. Its efficiency is tested on a simple
2-dimensional fermionic model.


title:
How to compute Green's Functions for entire Mass Trajectories within
  Krylov Solvers

abstract:
  The availability of efficient Krylov subspace solvers play a vital role for
the solution of a variety of numerical problems in computational science. Here
we consider lattice field theory. We present a new general numerical method to
compute many Green's functions for complex non-singular matrices within one
iteration process. Our procedure applies to matrices of structure $A=D-m$, with
$m$ proportional to the unit matrix, and can be integrated within any Krylov
subspace solver. We can compute the derivatives $x^{(n)}$ of the solution
vector $x$ with respect to the parameter $m$ and construct the Taylor expansion
of $x$ around $m$. We demonstrate the advantages of our method using a minimal
residual solver. Here the procedure requires $1$ intermediate vector for each
Green's function to compute. As real life example, we determine a mass
trajectory of the Wilson fermion matrix for lattice QCD. Here we find that we
can obtain Green's functions at all masses $\geq m$ at the price of one
inversion at mass $m$.


title:
On the scaling of the electroweak interface tension at finite
  temperature

abstract:
  We determine the interface tension of the finite-temperature electroweak
phase transition in a numerical investigation of the SU(2)--Higgs model on a
four-dimensional lattice with temporal extension $L_t=3$. In this simulation
the chosen parameters correspond to a Higgs boson mass of about 16 GeV. As a
result the interface tension shows only small scaling violations in comparison
with previous studies for $L_t=2$ lattices. We also report on some experiences
with autocorrelations in the applied Monte Carlo simulations of two-phase
systems.


title: Hybrid Molecular Dynamics for Lattice Supersymmetry

abstract:
  We present the first results obtained with a Hybrid Molecular Dynamics
algorithm applied to an $N=1$ SU(2) Super-Yang--Mills on the lattice. We derive
the Hamilton equations of motion for the system with Wilson gluinos and present
preliminary results on small lattices.


title: Simulating the massive Schwinger model with chiral defect fermions

abstract:
  Some time ago Kaplan proposed a new model for the description of chiral
fermions on the lattice by adding an extra dimension for the fermions. A
variant of this proposal was introduced by Shamir and can be used to describe
vector-like theories in even dimensions. We used this model for the simulation
of the massive Schwinger model at different gauge couplings. The prediction
that the fermion mass gets only multiplicative renormalization was tested and
verified.


title:
QCDF90: A set of Fortran 90 modules for a high-level, efficient
  implementation of QCD simulations

abstract:
  We present a complete set of Fortran 90 modules that can be used to write
very compact, efficient, and high level QCD programs. The modules define fields
(gauge, fermi, generators, complex, and real fields) as abstract data types,
together with simpler objects such as SU(3) matrices or color vectors.
Overloaded operators are then defined to perform all possible operations
between the fields that may be required in a QCD simulation. QCD programs
written using these modules need not have cumbersome subroutines and can be
very simple and transparent. This is illustrated with two simple example
programs.


title:
Topological susceptibility at zero and finite $T$ in SU(3) Yang-Mills
  theory

abstract:
  We determine the topological susceptibility $\chi$ at T=0 in pure SU(3) gauge
theory and its behaviour at finite $T$ across the deconfining transition. We
use an improved topological charge density operator. $\chi$ drops sharply by
one order of magnitude at the deconfining temperature $T_c$.


title: Vacuum State of Lattice Gauge Theory with Fermions in 2+1 Dimensions

abstract:
  We investigate the vacuum state of the lattice gauge theory with fermions in
2+1 dimensions. The vacuum in the Hermite form for the fermion part is
obtained; the vacuum in the unitary form has been proposed by Luo and Chen. It
is shown that the Hermite vacuum has a lower energy than the unitary one
through the variational method.


title: Dynamics of Clusters in Two-dimensional Potts Model

abstract:
  Dynamical behavior of the clusters during relaxation is studied in
two-dimensional Potts model using cluster algorithm. Average cluster size and
cluster formation velocity are calculated on two different lattice sizes for
different number of states during initial stages of the Monte Carlo simulation.
Dependence of these quantities on the order of the transition provides an
efficient method to study nature of the phase transitions occuring in similar
models.


title:
Chern-Simons Diffusion Rate near the Electroweak Phase Transition for
  $m_H \approx m_W$

abstract:
  The rate of $B$-violation in the standard model at finite temperature is
closely related to the diffusion rate $\Gamma$ of Chern-Simons number. We
compute this rate for $m_H \approx m_W$ in the classical approximation in an
effective SU(2)-Higgs model, using Krasnitz's algorithm. The parameters in the
effective hamiltonian are determined by comparison with dimensional reduction.
In the high temperature phase we find $\Gamma/V (\alpha_W T)^4 \approx 1$,
neglecting a finite renormalization. In the low temperature phase near the
transition we find the rate to be much larger than might be expected from
previous analytic calculations based on the sphaleron.


title: New fixed point action for SU(3) lattice gauge theory

abstract:
  We present a new fixed point action for SU(3) lattice gauge theory, which has
--- compared to earlier published fixed point actions --- shorter interaction
range and smaller violations of rotational symmetry in the static
$q\bar{q}$-potential even at shortest distances.


title:
Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The
  Two-Dimensional 3-State Potts Model Revisited

abstract:
  We have performed a high-precision Monte Carlo study of the dynamic critical
behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts
model. We find that the Li-Sokal bound ($\tau_{int,E} \geq const \times C_H$)
is almost but not quite sharp. The ratio $\tau_{int,E} / C_H$ seems to diverge
either as a small power ($\approx 0.08$) or as a logarithm.


title: Instantons or Monopoles? Dyons

abstract:
  Non-abelian gauge theories can be cast into abelian gauge theories with
monopoles. We ask what becomes of the instantons after abelian projection.
Instantons are found to consist of closed dyon loops. It is shown that the
electric charge of the dyons is quantized. The implication of this result for
the dynamics of the Yang-Mills vacuum is briefly discussed.


title: Phase transition in fluctuating branched geometry

abstract:
  We study grand--canonical and canonical properties of the model of branched
polymers proposed in \cite{adfo}. We show that the model has a fourth order
phase transition and calculate critical exponents. At the transition the
exponent $\gamma$ of the grand-canonical ensemble, analogous to the string
susceptibility exponent of surface models, $\gamma \sim 0.3237525...$ is the
first known example of positive $\gamma$ which is not of the form $1/n,\,
n=2,3,\ldots$. We show that a slight modification of the model produces a
continuos spectrum of $\gamma$'s in the range $(0,1/2]$ and changes the order
of the transition.


title: Lattice Gauge Theory of Three Dimensional Thirring Model

abstract:
  Three dimensional Thirring model with $N$ four-component Dirac fermions,
reformulated as a lattice gauge theory, is studied by computer simulation.
According to an $8^{3}$ data and preliminary $16^3$ data, chiral symmetry is
found to be spontaneously broken for $N=2,\;4$ and 6. $N=2$ data exhibits long
tail of the non-vanishing chiral condensate into weak coupling region, and
$N=6$ case shows phase separation between the strong coupling region and the
weak coupling region. Although the comparison between $8^3$ data and $16^3$
data shows large finite volume effects, an existence of the critical fermion
flavor number $N_{{\rm cr}}$ $(2<N_{{\rm cr}}<6)$ for which the chiral behavior
changes its character, is suggested by the current numerical data.


title:
Investigation of spontaneous symmetry breaking from a non standard
  approach

abstract:
  We propose a new method for the study of the chiral properties of the ground
state in Quantum Field Theories (QFT's) which is based on the computation of
the probability distribution function (p.d.f.) of the chiral condensate in the
chiral limit. We show how despite of the fact that Grassmann variables cannot
be simulated on a computer, an analysis of spontaneous symmetry breaking
without a symmetry breaking external field, which is standard in the case of
spin systems, can also be done in QFT's with fermion degrees of freedom.


title: Quarkonium Decay Matrix Elements from Quenched Lattice QCD

abstract:
  We calculate the long-distance matrix elements for the decays of the
lowest-lying S- and P-wave states of charmonium and bottomonium in quenched
lattice QCD, using a nonrelativistic formulation for the heavy quarks. (The
short-distance coefficients are known from perturbation theory.) In particular,
we present the first calculation from QCD first principles of the color-octet
contribution to P-wave decay---a contribution that is absent in potential
models. We also give the relations between the lattice matrix elements and
their continuum counterparts through one-loop order in perturbation theory.


title: Critical Exponents of the Classical Heisenberg Ferromagnet

abstract:
  In a recent letter, R.G. Brown and M. Ciftan (Phys. Rev. Lett. 76, 1352,
1996) reported high precision Monte Carlo (MC) estimates of the static critical
exponents of the classical 3D Heisenberg model, which stand in sharp contrast
to values obtained by four independent approaches, namely by other recent high
statistics MC simulations, high-temperature series analyses, field theoretical
methods, and experimental studies. In reply to the above cited work we
submitted this paper as a comment to Phys. Rev. Lett.


title: Orbitally excited and hybrid mesons from the lattice

abstract:
  We discuss in general the construction of gauge-invariant non-local meson
operators on the lattice. We use such operators to study the $P$- and $D$-wave
mesons as well as hybrid mesons in quenched QCD, with quark masses near the
strange quark mass. The resulting spectra are compared with experiment for the
orbital excitations. For the states produced by gluonic excitations (hybrid
mesons) we find evidence of mixing for non-exotic quantum numbers. We give
predictions for masses of the spin-exotic hybrid mesons with $J^{PC}=1^{-+},\
0^{+-}$, and $2^{+-}$.


title: Suppression of the negative sign problem in quantum Monte Carlo

abstract:
  We present a new Monte Carlo algorithm for simulating quantum spin systems
which is able to suppress the negative sign problem. This algorithm has only a
linear complexity in the lattice size used for the simulation. A general
description and a rigorous proof of its correctness is given. Its efficiency is
tested on a simple 2-dimensional fermionic model. For this model we show that
our algorithm eliminates the sign problem.


title: Lattice Simulations and Effective Theories

abstract:
  I present a brief introduction to the lattice formulation of quantum field
theory, and discuss the use of lattice simulations for studies in particle
physics phenomenology. The computation of $f_B$, the decay constant of the
$B$-meson, is used as a case study. I also explain the appearance and
cancellation of ``renormalons'' in the evaluation of power corrections
(higher-twist corrections) in hard scattering and decay processes.


title: Two-Flavor Staggered Fermion Thermodynamics at N_t = 12

abstract:
  We present results of an ongoing study of the nature of the high temperature
crossover in QCD with two light fermion flavors. These results are obtained
with the conventional staggered fermion action at the smallest lattice spacing
to date---approximately 0.1 fm. Of particular interest are a study of the
temperature of the crossover a determination of the induced baryon charge and
baryon susceptibility, the scalar susceptibility, and the chiral order
parameter, used to test models of critical behavior associated with chiral
symmetry restoration. From our new data and published results for N_t = 4, 6,
and 8, we determine the QCD magnetic equation of state from the chiral order
parameter using O(4) and mean field critical exponents and compare it with the
corresponding equation of state obtained from an O(4) spin model and mean field
theory. We also present a scaling analysis of the Polyakov loop, suggesting a
temperature dependent ``constituent quark free energy.''


title: Comparison of Inversion Algorithms for Wilson Fermions on the CM5

abstract:
  This talk presents results of a comparitive study of iterative algorithms
like minimal residue ($MR$) and conjugate gradient ($CG$, $BiCG\gamma_5$, and
\bicgstab) used for inverting the Dirac matrix $M$. The tests were done on the
Connection Machine CM-5 using $32^3 \times 64$ lattices. The fermion action
used is of Wilson type, both with and without the clover term. The overall
conclusion is that preconditioned over-relaxed $MR$ is the simplest, uses the
least memory, and is comparable in performance to \bicgstab. We find these two
algorithms to be equally robust, $i.e.$ insensitive to the starting solution
and to round-off errors.


title:
Finite Temperature Transitions in Lattice QCD with Wilson Quarks ---
  Chiral Transitions and the Influence of the Strange Quark ---

abstract:
  The nature of finite temperature transitions in lattice QCD with Wilson
quarks is studied near the chiral limit for the cases of 2, 3, and 6 flavors of
degenerate quarks ($N_F=2$, 3, and 6) and also for the case of massless up and
down quarks and a light strange quark ($N_F=2+1$). Our simulations mainly
performed on lattices with the temporal direction extension $N_t=4$ indicate
that the finite temperature transition in the chiral limit (chiral transition)
is continuous for $N_F=2$, while it is of first order for $N_F=3$ and 6. We
find that the transition is of first order for the case of massless up and down
quarks and the physical strange quark where we obtain a value of
$m_\phi/m_\rho$ consistent with the physical value. We also discuss the phase
structure at zero temperature as well as that at finite temperatures.


title:
The ${\cal O}(g^6)$ coefficient in the thermodynamic potential of hot
  SU(N) Gauge Theories and MQCD

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: Lattice gauge-fixing for generic covariant gauges

abstract:
  We propose a method which allows the generalization of the Landau lattice
gauge-fixing procedure to generic covariant gauges. We report preliminary
numerical results showing how the procedure works for $SU(2)$ and $SU(3)$. We
also report numerical results showing that the contribution of finite
lattice-spacing effects and/or spurious copies are relevant in the lattice
gauge-fixing procedure.


title:
Alpha_s from the non-perturbatively renormalised lattice three-gluon
  vertex

abstract:
  We compute the running QCD coupling on the lattice by evaluating two-point
and three-point off-shell gluon Green's functions in a fixed gauge and imposing
non-perturbative renormalisation conditions on them. Our exploratory study is
performed in the quenched approximation at beta=6.0 on 16^4 and 24^4 lattices.
We show that, for momenta in the range 1.8-2.3 Gev, our coupling runs according
to the two-loop asymptotic formula, allowing a precise determination of the
corresponding Lambda parameter. The role of lattice artifacts and finite-volume
effects is carefully analysed and these appear to be under control in the
momentum range of interest. Our renormalisation procedure corresponds to a
momentum subtraction scheme in continuum field theory, and therefore lattice
perturbation theory is not needed in order to match our results to the MSbar
scheme, thus eliminating a major source of uncertainty in the determination of
alpha_MSbar. Our method can be applied directly to the unquenched case.


title: Quenched Chiral Perturbation Theory for Baryons

abstract:
  We develop chiral perturbation theory for baryons in quenched QCD. Quenching
(the elimination of diagrams containing virtual quark loops) is achieved by
extending the Lagrangian method of Bernard and Golterman, and is implemented in
a theory where baryons are treated as fixed velocity sources. Our method
requires that the octet baryons be represented by a three index tensor rather
than by the usual matrix field. We calculate the leading non-analytic
corrections to the masses of octet and decuplet baryons. In QCD these are
proportional to $M_\pi^3$. We find that quenching alters the $M_\pi^3$ terms,
but does not completely remove them. In addition, we find non-analytic
contributions to baryon masses proportional to $M_\pi$ and $M_\pi^2 \log
M_\pi$. These terms, which are artifacts of quenching, dominate over the
$M_\pi^3$ terms for sufficiently small quark masses. We also point out various
pecularities of the quenched theory, most notably that the $\Delta$ baryon can
decay (if kinematically allowed), in the sense that its two point function will
be dominated at long Euclidean times by a nucleon plus pion intermediate state.


title: Seeking the Equation of State of Non-Compact Lattice QED

abstract:
  We perform a high statistics calculation of the equation of state for
non-compact QED on large lattices. The calculation extends to fermionic
correlation lengths of $\approx 8$, and it is combined with a finite size
scaling analysis of the lattice data.


title: Phase diagram of Regge quantum gravity coupled to SU(2) gauge theory

abstract:
  We analyze Regge quantum gravity coupled to SU(2) gauge theory on $4^3\times
2$, $6^{3}\times 4$ and $8^{3}\times 4$ simplicial lattices. It turns out that
the window of the well-defined phase of the gravity sector where geometrical
expectation values are stable extends to negative gravitational couplings as
well as to gauge couplings across the deconfinement phase transition. We study
the string tension from Polyakov loops, compare with the $\beta$-function of
pure gauge theory and conclude that a physical limit through scaling is
possible.


title:
Critical properties of the Antiferromagnetic \RP2$ model in three
  dimensions

abstract:
  We study the behavior of the antiferromagnetic RP$^2$ model in $d=3$. The
vacuum structure is analyzed in the critical and low temperature regions,
paying special attention to the spontaneous symmetry breaking pattern. Near the
critical point we observe a full breakdown of the O(3) symmetry of the action.
Several methods for computing critical exponents are compared. We conclude that
the most solid determination is obtained using a measure of the correlation
length. Corrections-to-scaling are parameterized, yielding a very accurate
determination of the critical coupling and a 5\% error measure of the related
exponent. This is used to estimate the systematic errors due to finite-size
effects.


title: Chiral symmetry and O(a) improvement in lattice QCD

abstract:
  The dominant cutoff effects in lattice QCD with Wilson quarks are
proportional to the lattice spacing a. In particular, the isovector axial
current satisfies the PCAC relation only up to such effects. Following a
suggestion of Symanzik, they can be cancelled by adding local O(a) correction
terms to the action and the axial current. We here address a number of
theoretical issues in connection with the O(a) improvement of lattice QCD and
then show that chiral symmetry can be used to fix the coefficients multiplying
the correction terms.


title: Light Quark Masses from Lattice QCD

abstract:
  We present estimates of the masses of light quarks using lattice data. Our
main results are based on a global analysis of all the published data for
Wilson, Sheikholeslami-Wohlert (clover), and staggered fermions, both in the
quenched approximation and with $n_f=2$ dynamical flavors. We find that the
values of masses with the various formulations agree after extrapolation to the
continuum limit for the $n_f=0$ theory. Our best estimates, in the MSbar scheme
at $\mu=2 GeV$, are $\mbar=3.4 +- 0.4 +- 0.3 MeV$ and $m_s = 100 +- 21 +- 10
MeV$ in the quenched approximation. The $n_f=2$ results, $\mbar = 2.7 +- 0.3 +-
0.3 MeV$ and $m_s = 68 +- 12 +- 7 MeV$, are preliminary. (A linear
extrapolation in $n_f$ would further reduce these estimates for the physical
case of three dynamical flavors.) These estimates are smaller than
phenomenological estimates based on sum rules, but maintain the ratios
predicted by chiral perturbation theory. The new results have a significant
impact on the extraction of $\epsilon'/\epsilon$ from the Standard Model. Using
the same lattice data we estimate the quark condensate using the
Gell-Mann-Oakes-Renner relation. Again the three formulations give consistent
results after extrapolation to $a=0$, and the value turns out to be
correspondingly larger, roughly preserving $m_s \vev{\bar \psi \psi}$.


title:
High-Temperature Properties of the Z(3) Interface in (2+1)-D SU(3) Gauge
  Theory

abstract:
  We study the high-temperature properties of the Z(3) interface which forms
between the various ordered phases of pure SU(3) gauge theory above a critical
temperature. On a (2+1)-D Euclidean lattice, we perform an accurate measurement
of the interface tension, which shows good agreement with the prediction of
perturbation theory. We also examine the behaviour of the Debye electric
screening mass, and compare this with theoretical predictions.


title: The Deconfinement Transition on Coarse Lattices

abstract:
  We compute the critical temperature $T_c$ for the deconfinement transition of
pure QCD on coarse lattices, with $N_t = 2, 3, 4$, and lattice spacings from
.33 fm to .15 fm. We employ a perturbatively improved gluon action designed to
remove order $a^2$ and $\alpha_s a^2$ errors. We find that $T_c$ in units of
the charmonium 1P--1S splitting and the torelon mass is independent of $a$ to
within approximately 5\%.


title:
3--Dimensional Lattice Studies of the Electroweak Phase Transition at
  M_{Higgs} approx 70 GeV

abstract:
  We study the electroweak phase transition by lattice simulations of an
effective 3--dimensional theory, for a Higgs mass of about 70 GeV. Exploiting,
among others, a variant of the equal weight criterion of phase equilibrium, we
obtain transition temperature, latent heat and surface tension, and compare
with M_H approx 35 GeV. In the broken phase masses and Higgs condensates are
compared to perturbation theory. For the symmetric phase, bound state masses
and the static force are determined.


title: Compact U(1) Lattice Gauge-Higgs Theory with Monopole Suppression

abstract:
  We investigate a model of a U(1)-Higgs theory on the lattice with compact
gauge fields but completely suppressed (elementary) monopoles. We study the
model at two values of the quartic Higgs self-coupling, a strong coupling,
$\lambda = 3.0$, and a weak coupling, $\lambda=0.01$. We map out the phase
diagrams and find that the monopole suppression eliminated the confined phase
of the standard lattice model at strong gauge coupling. We perform a detailed
analysis of the static potential and study the mass spectrum in the Coulomb and
Higgs phases for three values of the gauge coupling. We also probe the
existence of a scalar bosonium to the extent that our data allow and conclude
that further investigations are required in the Coulomb phase.


title: Evidence for eta prime - pion splitting in unquenched lattice QCD

abstract:
  We perform an extrapolation from negative to positive flavour numbers of full
QCD lattice estimates of the $\eta'$ mass. The extrapolations are carried out
by keeping $\rho$ and $\pi$ masses at fixed values. We find an $\eta'$ -- $\pi$
splitting which shows a flavour dependence consistent with the Witten Veneziano
formula based on the $U(1)$ anomaly. The quantitative splitting is consistent
with the estimates made in the quenched approximation.


title: Monopoles at Finite Volume and Temperature in SU(2) Lattice Gauge Theory

abstract:
  We resolve a discrepancy between the SU(2) spacial string tension at finite
temperature, and the value obtained by monopoles in the maximum Abelian gauge.
Previous work had incorrectly omitted a term due to Dirac sheets. When this
term is included, the monopole and full SU(2) determinations of the spacial
string tension agree to within the statistical errors of the monopole
calculation.


title: Properties of QCD vacuum from lattice

abstract:
  A disorder parameter is constructed which signals the condensation of
vortices. The construction is tested by numerical simulations. Advances in the
understanding of the basic properties of QCD vacuum will be reported. Three
main subjects will be touched: 1) Condensation of monopoles and confinement. 2)
Topology, or instanton physics. 3) Gauge invariant field strength correlators,
and their behaviour across the deconfining phase transition.


title:
Non-perturbative determination of beta-functions and excited string
  states from lattices

abstract:
  We use lattice sum rules for the static quark potential to determine the
beta-function for symmetric and asymmetric lattices non-perturbatively. We also
study the colour field distributions in excited gluonic states.


title:
Efficiency of different matrix inversion methods applied to Wilson
  fermions

abstract:
  We compare different conjugate gradient -- like matrix inversion methods (CG,
BiCGstab1 and BiCGstab2) employing for this purpose the compact lattice quantum
electrodynamics (QED) with Wilson fermions. The main goals of this
investigation are the CPU time efficiency of the methods as well as the
influence of machine precision on the reliability of (physical) results
especially close to the 'critical' line $~\kappa_c(\bt)$.


title: Instabilities and Non-Reversibility of Molecular Dynamics Trajectories

abstract:
  The theoretical justification of the Hybrid Monte Carlo algorithm depends
upon the molecular dynamics trajectories within it being exactly reversible. If
computations were carried out with exact arithmetic then it would be easy to
ensure such reversibility, but the use of approximate floating point arithmetic
inevitably introduces violations of reversibility. In the absence of evidence
to the contrary, we are usually prepared to accept that such rounding errors
can be made small enough to be innocuous, but in certain circumstances they are
exponentially amplified and lead to blatantly erroneous results. We show that
there are two types of instability of the molecular dynamics trajectories which
lead to this behavior, instabilities due to insufficiently accurate numerical
integration of Hamilton's equations, and intrinsic chaos in the underlying
continuous fictitious time equations of motion themselves. We analyze the
former for free field theory, and show that it is essentially a finite volume
effect. For the latter we propose a hypothesis as to how the Liapunov exponent
describing the chaotic behavior of the fictitious time equations of motion for
an asymptotically free quantum field theory behaves as the system is taken to
its continuum limit, and explain why this means that instabilities in molecular
dynamics trajectories are not 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 confirm some of our
results.


title: Light Hadron Masses on Coarse Lattices with Improved Actions

abstract:
  The lattice QCD field is currently undergoing a revolution in the manner in
which improvements of the approach are being implemented. We are examining the
utility of order-a^2-improved tadpole-improved actions for the light fermion
sector. The masses of the low-lying hadrons are calculated using the
order-a^2-improved gluon action and the order-a^2-improved 2-link fermion
action of Hamber and Wu with further tadpole improvement. Initial results on a
6^3 x 12 lattice at beta = 6.25 and a 10^3 x 16 lattice at beta = 7.0 are
presented. The corresponding lattice spacings are approximately 0.40 fm and
0.24 fm respectively. These lattices provide a constant volume in which the
scaling of observables is assessed.


title: Tensor Charge of the Nucleon on the Lattice

abstract:
  Tensor charge of the nucleon, which will be measured in Drell-Yan processes
in polarized proton-proton collisions at RHIC, are studied in quenched lattice
QCD simulation. On the 16$^3\times$ 20 lattice with $\beta=5.7$, connected
parts of the tensor charge are determined with small statistical error, while
the disconnected parts are found to be small with relatively large error bars.
Flavor-singlet tensor charge ($\delta \Sigma = \delta u + \delta d + \delta s$)
is not suppressed as opposed to the flavor singlet axial charge ($\Delta \Sigma
= \Delta u + \Delta d + \Delta s$).


title: Gribov Copies in the Maximally Abelian Gauge and Confinement

abstract:
  We fix $SU(2)$ lattice gauge fields to the Maximally Abelian gauge in both
three and four dimensions. We extract the corresponding $U(1)$ fields and
monopole current densities and calculate separately the confining string
tensions arising from these $U(1)$ fields and monopole `condensates'. We
generate multiple Gribov copies and study how the $U(1)$ fields and monopole
distributions vary between these different copies. As expected, we find
substantial variations in the number of monopoles, their locations and in the
values of the $U(1)$ field strengths. The string tensions extracted from
`extreme' Gribov copies also differ but this difference appears to be no more
than about 20\%. We also directly compare the fields of different Gribov
copies. We find that on the distance scales relevant to confinement the $U(1)$
and monopole fluxes that disorder Wilson loops are highly correlated between
these different Gribov copies. All this suggests that while there is indeed a
Gribov copy problem the resulting ambiguity is, in this gauge and for the study
of confinement, of limited importance.


title: Glueballs from Improved Lattice Actions

abstract:
  The low-lying glueball masses and the hadronic scale $r_0$ are computed in
lattice SU(3) gauge theory with the aim of establishing the effectiveness of
the improved action approach in removing finite-spacing artifacts. The use of
anisotropic lattices in which the temporal spacing is much smaller than that in
the spatial directions allows much more efficient glueball mass measurements.


title: On the spectrum of the QCD Dirac operator

abstract:
  In this lecture we argue that the fluctuations of Dirac eigenvalues on the
finest scale, i.e. on the scale of the average level spacing do not depend on
the underlying dynamics and can be obtained from a chiral random matrix theory
with the same low energy effective theory. We present three pieces of evidence
supporting that such microscopic correlations of lattice QCD Dirac spectra are
given by chiral random matrix theory. First, we find that the spectral
correlations of eigenvalues in the bulk of the spectrum obey the
Dyson-Mehta-Wigner statistics. Second, we show that the valence quark mass
dependence for sufficiently small quark masses, as calculated by the Columbia
group, can be obtained from the microscopic spectral density of chiral random
matrix theory. Third, in the framework of chiral random matrix models, we
present results showing that the microscopic spectral density is strongly
universal, i.e. is insensitive to the details of the probability distribution.


title:
Non-Gaussian fixed point in four-dimensional pure compact U(1) gauge
  theory on the lattice

abstract:
  The line of phase transitions, separating the confinement and the Coulomb
phases in the four-dimensional pure compact U(1) gauge theory with extended
Wilson action, is reconsidered. We present new numerical evidence that a part
of this line, including the original Wilson action, is of second order. By
means of a high precision simulation on homogeneous lattices on a sphere we
find that along this line the scaling behavior is determined by one fixed point
with distinctly non-Gaussian critical exponent nu = 0.365(8). This makes the
existence of a nontrivial and nonasymptotically free four-dimensional pure U(1)
gauge theory in the continuum very probable. The universality and duality
arguments suggest that this conclusion holds also for the monopole loop gas,
for the noncompact abelian Higgs model at large negative squared bare mass, and
for the corresponding effective string theory.


title: Relations Between Monopoles, Instantons and Chiral Condensate

abstract:
  We analyze the interplay of topological objects in four dimensional QCD. The
distributions of color magnetic monopoles obtained in the maximum abelian gauge
are computed around instantons in both pure and full QCD. We find an enhanced
probability of encountering monopoles inside the core of an instanton on gauge
field average. For specific gauge field configurations we visualize the
situation graphically. Moreover we investigate how monopole loops and
instantons are locally correlated with the chiral condensate.


title: Geometrical Interpretation of the KPZ Exponents

abstract:
  We provide evidence that the KPZ exponents in two-dimensional quantum gravity
can be interpreted as scaling exponents of correlation functions which are
functions of the invariant geodesic distance between the fields.


title: Four-dimensional pure compact U(1) gauge theory on a spherical lattice

abstract:
  We investigate the confinement-Coulomb phase transition in the
four-dimensional (4D) pure compact U(1) gauge theory on spherical lattices. The
action contains the Wilson coupling beta and the double charge coupling gamma.
The lattice is obtained from the 4D surface of the 5D cubic lattice by its
radial projection onto a 4D sphere, and made homogeneous by means of
appropriate weight factors for individual plaquette contributions to the
action. On such lattices the two-state signal, impeding the studies of this
theory on toroidal lattices, is absent for gamma le 0. Furthermore, here a
consistent finite-size scaling behavior of several bulk observables is found,
with the correlation length exponent nu in the range nu = 0.35 - 40. These
observables include Fisher zeros, specific-heat and cumulant extrema as well as
pseudocritical values of beta at fixed gamma. The most reliable determination
of nu by means of the Fisher zeros gives nu = 0.365(8). The phase transition at
gamma le 0 is thus very probably of 2nd order and belongs to the universality
class of a non-Gaussian fixed point.


title:
Gauge fixing, zero--momentum modes and the calculation of masses on a
  lattice

abstract:
  It is shown that the zero--momentum modes can strongly affect the values of
the masses, for example the magnetic screening mass $m_m$, calculated from
gauge--dependent correlators with zero momentum.


title: Dual Lattice Blockspin Transformation and Monopole condensation in QCD

abstract:
  Recent studies of confinement based on the idea of abelian monopole
condensation are reviewed briefly. Emphasis is placed on the approach to get
the effective monoole action using the blockspin transformation on the dual
lattice. The trajectory obtained looks to be the renormalized one in $SU(2)$
QCD. A disorder parameter of confinement is constructed. Monopole condensation
occurs also in $SU(3)$ QCD.


title:
O(a) improvement of the axial current in lattice QCD to one-loop order
  of perturbation theory

abstract:
  The conservation of the isovector axial current in lattice QCD with massless
Wilson quarks is studied to one-loop order of perturbation theory. Following a
strategy described in a previous publication, the O($a$) counterterm required
for on-shell improvement of the current is computed. We also confirm an earlier
result of Wohlert for the coefficient in front of the SW term in the improved
action.


title: Antiferromagnetic 4-d O(4) Model

abstract:
  We study the phase diagram of the four dimensional O(4) model with first
(beta1) and second (beta2) neighbor couplings, specially in the beta2 < 0
region, where we find a line of transitions which seems to be second order. We
also compute the critical exponents on this line at the point beta1 =0 (F4
lattice) by Finite Size Scaling techniques up to a lattice size of 24, being
these exponents different from the Mean Field ones.


title:
Dual vortices and gauge choice in Abelian projected SU(2) lattice gauge
  theory

abstract:
  We explore vortex formation for Abelian projected SU(2) in the Polyakov gauge
and compare the results with those calculated in the maximal Abelian gauge. In
both gauges, a non-zero vacuum expectation value of a monopole field operator
signals confinement. We find vortices in the Polyakov projection, confirming
the connection between the dual superconductor order parameter and the
existence of vortices. However we find that the Polyakov Abelian projection is
problematic, leaving the maximal Abelian projection as the best candidate to
define an effective theory of confinement in this scenario.


title: Lattice Charge Overlap II: Aspects of Charged Pion Polarizability

abstract:
  Formulas are developed for use in lattice studies of charged hadron
polarizabilities. In particular, the valence quark different-flavor component
of the charged pion polarizability is examined on a $16^{3}\times 24$ lattice
at $\beta=6.0$ using Wilson fermions. Using the elastic limit results of Part I
of this series, it is concluded that this represents a small negative component
of the full charged polarizabilty.


title: Adaptive Step Size for Hybrid Monte Carlo Algorithm

abstract:
  We implement an adaptive step size method for the Hybrid Monte Carlo a
lgorithm. The adaptive step size is given by solving a symmetric error
equation. An integr ator with such an adaptive step size is reversible.
Although we observe appreciable variations of the step size, the overhead of
the method exceeds its benefits. We propose an explanation for this phenomenon.


title:
Domain walls and perturbation theory in high temperature gauge theory:
  SU(2) in 2+1 dimensions

abstract:
  We study the detailed properties of Z_2 domain walls in the deconfined high
temperature phase of the d=2+1 SU(2) gauge theory. These walls are studied both
by computer simulations of the lattice theory and by one-loop perturbative
calculations. The latter are carried out both in the continuum and on the
lattice. We find that leading order perturbation theory reproduces the detailed
properties of these domain walls remarkably accurately even at temperatures
where the effective dimensionless expansion parameter, g^2/T, is close to
unity. The quantities studied include the surface tension, the action density
profiles, roughening and the electric screening mass. It is only for the last
quantity that we find an exception to the precocious success of perturbation
theory. All this shows that, despite the presence of infrared divergences at
higher orders, high-T perturbation theory can be an accurate calculational
tool.


title: Monopole Spectra in non-Abelian Gauge Theories

abstract:
  We study the continuum limit of the length spectrum of magnetic monopole
structures found after various Abelian projections of pure gauge SU(2),
including the maximally Abelian gauge. We comment on Gribov copies, and
measurements of the string tension.


title: Invariant measure in hot gauge theories

abstract:
  We investigate properties of the invariant measure for the $A_0$ gauge field
in finite temperature gauge theories both on the lattice and in the continuum
theory. We have found the cancellation of the naive measure in both cases. The
result is quite general and holds at any finite temperature. We demonstrate,
however, that there is no cancellation at any temperature for the invariant
measure contribution understood as Z(N) symmetrical distribution of gauge field
configurations. The spontaneous breakdown of Z(N) global symmetry is entirely
due to the potential energy term of the gluonic interaction in the effective
potential. The effects of this measure on the effective action, mechanism of
confinement and $A_0$ condensation are discussed.


title:
Evidence for a first order transition in a plaquette 3d Ising-like
  action

abstract:
  We investigate a 3d Ising action which corresponds to a a class of models
defined by Savvidy and Wegner, originally intended as discrete versions of
string theories on cubic lattices. These models have vanishing bare surface
tension and the couplings are tuned in such a way that the action depends only
on the angles of the discrete surface, i.e. on the way the surface is embedded
in ${\bf Z}^3$. Hence the name gonihedric by which they are known. We show that
the model displays a rather clear first order phase transition in the limit
where self-avoidance is neglected and the action becomes a plaquette one. This
transition persists for small values of the self avoidance coupling, but it
turns to second order when this latter parameter is further increased. These
results exclude the use of this type of action as models of gonihedric random
surfaces, at least in the limit where self avoidance is neglected.


title: Gonihedric Ising Actions

abstract:
  We discuss a generalized Ising action containing nearest neighbour, next to
nearest neighbour and plaquette terms that has been suggested as a potential
string worldsheet discretization on cubic lattices by Savvidy and Wegner. This
displays both first and second order transitions depending on the value of a
``self-intersection'' coupling as well as possessing a novel semi-global
symmetry.


title: $B$ Decay Constants from NRQCD with Dynamical Fermions

abstract:
  We present a lattice investigation of the heavy-light meson decay constants
using Wilson light quarks and NRQCD heavy quarks, partially including the
effects of dynamical sea quarks. We calculate the pseudoscalar and vector decay
constants over a wide range in heavy quark mass and are able to perform a
detailed analysis of heavy quark symmetry. We find consistency between the
extrapolation of the NRQCD results and the static case, as expected. We find
the slope of the decay constants with $1/M$ is significantly larger than naive
expectations and the results of previous lattice calculations. For the first
time we extract the non-perturbative coefficients of the slope arising from the
$O(1/M)$ heavy quark interactions separately and show the kinetic energy of the
heavy quark is dominant and responsible for the large slope. In addition, we
find that significant systematic errors remain in the decay constant extracted
around the $B$ meson mass due to truncating the NRQCD series at $O(1/M)$. We
estimate the higher order contributions to $f_B$ are approximately $20\%$;
roughly the same size as the systematic errors introduced by using the Wilson
action for light quarks.


title: Critical properties of the Z(3) interface in (2+1)-D SU(3) gauge theory

abstract:
  We study the interface between two different Z(3) vacua in the deconfined
phase of SU(3) pure gauge theory in 2+1 dimensions just above the critical
temperature. In simulations of the Euclidean lattice gauge theory formulation
of the system we measure the fluctuations of the interface as the critical
temperature is approached and as a function of system size. We show that the
intrinsic width of the interface remains small even very close to the critical
temperature. Some dynamical exponents which govern the interaction of the
interface with our Monte Carlo algorithm are also estimated. We conclude that
the Z(3) interface has properties broadly similar to those in many other
comparable statistical mechanical systems.


title: Physics From Breit-Frame Regularization Of a Lattice Hamiltonian

abstract:
  We suggest a Hamiltonian formulation on a momentum lattice using a physically
motivated regularization using the Breit-frame which links the maximal parton
number to the lattice size. This scheme restricts parton momenta to positive
values in each spatial direction. This leads to a drastic reduction of degrees
of freedom compared to a regularization in the rest frame (center at zero
momentum). We discuss the computation of physical observables like (i) mass
spectrum in the critical region, (ii) structure and distribution functions,
(iii) $S$-matrix, (iv) finite temperature and finite density thermodynamics in
the Breit-frame regularization. For the scalar $\phi^{4}_{3+1}$ theory we
present numerical results for the mass spectrum in the critical region. We
observe scaling behavior for the mass of the ground state and for some higher
lying states. We compare our results with renormalization group results by
L\"uscher and Weisz. Using the Breit-frame, we calculate for $QCD$ the relation
between the $W^{\mu \nu}$ tensor, structure functions (polarized and
unpolarized) and quark distribution functions. We use the improved parton-model
with a scale dependence and take into account a non-zero parton mass. In the
Bjorken limes we find the standard relations between $F_{1}$, $F_{2}$, $g_{1}$
and the quark distribution functions. We discuss the r\^ole of helicity. We
present numerical results for parton distribution functions in the scalar
model. For the $\phi^{4}$-model we find no bound state with internal parton
structure. For the $\phi^{3}$-model we find a distribution function with parton
structure similar to Altarelli-Parisi behavior of $QCD$.


title: Testing Improved Actions

abstract:
  We discuss testing improved actions in the context of finite volume gauge
theories, where both results for the continuum and the Wilson lattice action
are known analytically for volumes up to 0.7 fermi across. A new improved
action is introduced, obtained by adding a 2 x 2 plaquette to the
L\"uscher-Weisz Symanzik action, for which the gauge field propagator greatly
simplifies. We call this the square Symanzik action. We present the tree-level
parameters of this improved action and the value of its Lambda parameter. We
also give some Monte Carlo results and discuss some of the issues related to
violations of unitarity at the scale of the lattice cutoff due to
next-to-nearest coupling in the time direction.


title: Distribution Functions From Breit-Frame Regularisation

abstract:
  We suggest a new Hamiltonian lattice approach, using a regularisation
motivated by deep inelastic scattering. We discuss the relation between
distribution functions and the $F_1$ structure function. We have tested this
method by computing the critical behaviour of the scalar model and find
agreement with scaling behaviour and with results by L\"uscher and Weisz.


title: Critical behavior and monopole density in U(1) lattice gauge theory

abstract:
  Our study of the energy distribution has shown that the strength of the first
order transition in the four-dimensional compact U(1) lattice gauge theory
decreases when the coupling $\lambda$ of the monopole term increases. The
disappearance of the energy gap for sufficiently large values of $\lambda$
indicates that the transition ultimately becomes of second order. In our
present investigation, based on a finite-size analysis, we show that already at
$\lambda= 0.9$ the critical exponent is characteristic of a second-order
transition. Interestingly, this exponent turns out to be definitely different
from that of the Gaussian case. We observe that the monopole density becomes
constant in the second order region. In addition we find the rather surprising
result that the phase transition persists up to very large values of $\lambda$,
where the transition moves to (large) negative $\beta$.


title:
Algebraic algorithm for the computation of one-loop Feynman diagrams in
  lattice QCD with Wilson fermions

abstract:
  We describe an algebraic algorithm which allows to express every one-loop
lattice integral with gluon or Wilson-fermion propagators in terms of a small
number of basic constants which can be computed with arbitrary high precision.
Although the presentation is restricted to four dimensions the technique can be
generalized to every space dimension. Various examples are given, including the
one-loop self-energies of the quarks and gluons and the renormalization
constants for some dimension-three and dimension-four lattice operators. We
also give a method to express the lattice free propagator for Wilson fermions
in coordinate space as a linear function of its values in eight points near the
origin. This is an essential step in order to apply the recent methods of
L\"{u}scher and Weisz to higher-loop integrals with fermions.


title: Bayesian Analysis of Many-Pole Fits of Hadron Propagators in Lattice QCD

abstract:
  We use Bayes' probability theorem to analyze many-pole fits of hadron
propagators. An alternative method of estimating values and uncertainties of
the fit parameters is offered, which has certain advantages over the
conventional methods. The probability distribution of the parameters of a fit
is calculated. The relative probability of various models is calculated.


title:
How to compute one-loop Feynman diagrams in lattice QCD with Wilson
  fermions

abstract:
  We describe an algebraic algorithm which allows to express every one-loop
lattice integral with gluon or Wilson-fermion propagators in terms of a small
number of basic constants which can be computed with arbitrary high precision.
Although the presentation is restricted to four dimensions the technique can be
generalized to every space dimension. We also give a method to express the
lattice free propagator for Wilson fermions in coordinate space as a linear
function of its values in eight points near the origin. This is an essential
step in order to apply the recent methods of L\" uscher and Weisz to
higher-loop integrals with fermions.


title: Corrections to finite-size scaling in two-dimensional O(N) sigma-models

abstract:
  We have considered the corrections to the finite-size-scaling functions for a
general class of $O(N)$ $\sigma$-models with two-spin interactions in two
dimensions for $N=\infty$. We have computed the leading corrections finding
that they generically behave as $(f(z) \log L + g(z))/L^2$ where $z = m(L) L$
and $m(L)$ is a mass scale; $f(z)$ vanishes for Symanzik improved actions for
which the inverse propagator behaves as $q^2 + O(q^6)$ for small $q$, but not
for on-shell improved ones. We also discuss a model with four-spin interactions
which shows a much more complicated behaviour.


title: Soft Covariant Gauges on the Lattice

abstract:
  We present an exploratory study of a one-parameter family of covariant,
non-perturbative lattice gauge-fixing conditions, that can be implemented
through a simple Monte Carlo algorithm. We demonstrate that at the numerical
level the procedure is feasible, and as a first application we examine the
gauge dependence of the gluon propagator.


title: Lattice Background Effective Action: a Proposal

abstract:
  We propose a method based on the Schr\"odinger functional for computing on
the lattice the gauge invariant effective action for external background
fields. We check this method by studying the U(1) lattice gauge theory in
presence of a constant magnetic background field.


title: Interfaces in hot gauge theory

abstract:
  The string tension at low T and the free energy of domain walls at high T can
be computed from one and the same observable. We show by explicit calculation
that domain walls in hot Z(2) gauge theory have good thermodynamical behaviour.
This is due to roughening of the wall, which expresses the restoration of
translational symmetry.


title: The fermion determinant and the chiral gauge theory on a lattice

abstract:
  Considering as an example a simple lattice ansatz for the chiral fermion
determinant, we demonstrate that even very mild violation of gauge invariance
by the determinant at finite lattice spacing leads to the need for another
scale in the full gauge theory. This new scale is much grater than the lattice
spacing and is associated with the gauge variables.


title: A High Statistics Lattice Calculation of The B-meson Binding Energy

abstract:
  We present a high statistics lattice calculation of the B--meson binding
energy $\overline{\Lambda}$ of the heavy--quark inside the pseudoscalar
B--meson. Our numerical results have been obtained from several independent
numerical simulations at $\beta=6.0$, $6.2$ and $6.4$, and using, for the meson
correlators, the results obtained by the APE group at the same values of
$\beta$. Our best estimate, obtained by combining results at different values
of $\beta$, is $\overline{\Lambda}=180^{+30}_{-20}$ MeV. For the
$\overline{MS}$ running mass, we obtain
$\overline{m}_{b}(\overline{m}_{b})=4.15 \pm 0.05 \pm 0.20$ GeV, in reasonable
agreement with previous determinations. The systematic error is the truncation
of the perturbative series in the matching condition of the relevant operator
of the Heavy Quark Effective Theory.


title: Lattice DIS Structure Functions

abstract:
  We present the computation, in lattice QCD, of the renormalization constants
and mixing coefficients of operators that measure the first two moments of DIS
Structure Functions. These calculations have been performed using the
Sheikholeslami-Wohlert O(a) improved ``clover'' action, which is known to
reduce the systematic error associated with the finiteness of the lattice
spacing a. Due to the complexities of the computations, we have developed,
using the computer languages Schoonschip and Form, general codes that are able
to automatically carry out all the analytic lattice manipulations.


title: Finite Size Analysis of the U(1) Background Field Effective Action

abstract:
  We apply the finite size scaling analysis to the derivative of the density of
the effective action for the lattice U(1) pure gauge theory in an external
constant magnetic field. We found the presence of a continuous phase
transition. Moreover, our extimate of of the critical parameters gives values
consistent with those extracted from the analysis of the specific heat.


title: Gravity and Random Surfaces on the Lattice - A Review

abstract:
  We review recent work in the lattice approach to random surfaces and quantum
gravity. Our task is made somewhat easier by some very interesting results,
particularly in four dimensions, that have appeared recently and which are
reported elsewhere in these proceedings. Inevitably, given the scope of the
review and the limitations of space, the presentation will omit work of
importance and be telegraphic in discussing work that is included, for which
apologies are offered in advance. After the customary brief historical
introduction we work our way in dimensional order from one up to four
dimensions before closing with some remarks on the relation, if any, between
the various lattice models and ``real'' 4D gravity.