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

We apply a new coordinate space method for the evaluation of lattice Feynman diagrams suggested by L\"uscher and Weisz to field theories in two dimensions. Our work is to be presented for the theories with massless propagators. The main idea is to deal with the integrals in position space by making use of the recursion relation for the free propagator $G(x)$ which allows to compute the propagator recursively by its values around origin. It turns out that the method is very efficient and gives very precise results. We illustrate the technique by evaluating a number of two- and three-loop diagrams explicitly.Comment: 25 pages, Latex, 2 figures, revised by discussing some points in more detail and correcting a few typo

The ground state of three quarks

We measure the static three-quark potential in SU(3) lattice gauge theory with improved accuracy, by using all available technical refinements, including Luscher-Weisz exponential variance reduction. Together with insight gained from 3-state Potts model simulations, our results allow us to sort out the merits of the Delta- and Y-ansaetze.Comment: 3 pages, 4 figures, talk presented at Lattice2002(topology

Lattice QCD with Exponentially Small Chirality Breaking

A new multifermion formulation of lattice QCD is proposed. The model is free of spectrum doubling and preserves all nonanomalous chiral symmetries up to exponentially small corrections. It is argued that a small number of fermion fields may provide a good approximation making computer simulations feasible.Comment: 14 pages, no figures; typos correcte

Glueballs on the three-sphere

We study the non-perturbative effects of the global features of the configuration space for SU(2) gauge theory on the three-sphere. The strategy is to reduce the full problem to an effective theory for the dynamics of the low-energy modes. By explicitly integrating out the high-energy modes, the one-loop correction to the effective hamiltonian is obtained. Imposing the $\theta$ dependence through boundary conditions in configuration space incorporates the non-perturbative effects of the non-contractable loops in the full configuration space. After this we obtain the glueball spectrum of the effective theory with a variational method.Comment: 48 p LaTeX, 13 Postscript figures appende

Deconfinement and Percolation

Using percolation theory, we derive a conceptual definition of deconfinement in terms of cluster formation. The result is readily applicable to infinite volume equilibrium matter as well as to finite size pre-equilibrium systems in nuclear collisions.Comment: 13 pages, latex, six figures include

Matrix Model and Ginsparg-Wilson Relation

We discuss that the Ginsparg-Wilson relation, which has the key role in the recent development of constructing lattice chiral gauge theory, can play an important role to define chiral structures in finite matrix models and noncommutative geometries.Comment: Latex 3 pages, To appear in Nucl.Phys.Proc.Suppl. of Lattice2003(chiral), Tsukuba, Japan, Jul.15-19, 200

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

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 $8\pi^2/g^2$.Comment: uufiles plain latex mss, epsf figures appended as .eps file

f_B and two scales problems in lattice QCD

A novel method to calculate f_B on the lattice is introduced, based on the study of the dependence of finite size effects upon the heavy quark mass of flavoured mesons and on a non-perturbative recursive finite size technique. We avoid the systematic errors related to extrapolations from the static limit or to the tuning of the coefficients of effective Lagrangian and the results admit an extrapolation to the continuum limit. We perform a first estimate at finite lattice spacing, but close to the continuum limit, giving f_B = 170(11)(5)(22) MeV. We also obtain f_{B_s} = 192(9)(5)(24) MeV. The first error is statistical, the second is our estimate of the systematic error from the method and the third the systematic error from the specific approximations adopted in this first exploratory calculation. The method can be generalized to two--scale problems in lattice QCD.Comment: 16 pages, 5 figures. Accepted for publication by Phys.Lett.B. Revised version, discussion on systematic errors added, results unchange

Quenched QCD with fixed-point and chirally improved fermion

In this contribution we present results from quenched QCD simulations with the parameterized fixed-point (FP) and the chirally improved (CI) Dirac operator. Both these operators are approximate solutions of the Ginsparg-Wilson equation and have good chiral properties. We focus our discussion on observables sensitive to chirality. In particular we explore pion masses down to 210 MeV in light hadron spectroscopy, quenched chiral logs, the pion decay constant and the pion scattering length. We discuss finite volume effects, scaling properties of the FP and CI operators and performance issues in their numerical implementation.Comment: Lattice2002(chiral), 17 pages, 21 figures, (LaTeX style file espcrc2.sty and AMS style files