Two-particle wave function in four dimensional Ising model

An exploratory study of two-particle wave function is carried out with a four dimensional simple model. The wave functions not only for two-particle ground and first excited states but also for an unstable state are calculated from three- and four-point functions using the diagonalization method suggested by L\"uscher and Wolff. The scattering phase shift is evaluated from these wave functions.Comment: Poster presented at Lattice2004(spectrum), Fermilab, June 21-26, 200

Nonperturbatively Improved Hadron Spectroscopy Near the Continuum Limit

We report the results of our quenched lattice simulations of the Wilson action with a nonperturbatively determined clover term at beta=6.2 and compare them with those of the standard Wilson action at the same beta value.Comment: 3 pages, including 3 figures; talk given at LATTICE9

Volume dependence of light hadron masses in full lattice QCD

The aim of the GRAL project is to simulate full QCD with standard Wilson fermions at light quark masses on small to medium-sized lattices and to obtain infinite-volume results by extrapolation. In order to establish the functional form of the volume dependence we study systematically the finite-size effects in the light hadron spectrum. We give an update on the status of the GRAL project and show that our simulation data for the light hadron masses depend exponentially on the lattice size.Comment: 3 pages, 1 figure, Lattice2003(spectrum

A perturbative determination of O(a) boundary improvement coefficients for the Schr\"odinger Functional coupling at 1-loop with improved gauge actions

We determine O($a$) boundary improvement coefficients up to 1-loop level for the Schr\"odinger Functional coupling with improved gauge actions including plaquette and rectangle loops. These coefficients are required to implement 1-loop O($a$) improvement in full QCD simulations for the coupling with the improved gauge actions. To this order, lattice artifacts of step scaling function for each improved gauge action are also investigated. In addition, passing through the SF scheme, we estimate the ratio of $\Lambda$-parameters between the improved gauge actions and the plaquette action more accurately.Comment: 17 pages, 2 figures, 6 table

Renormalization of lattice gauge theories with massless Ginsparg Wilson fermions

Using functional techniques, we prove, to all orders of perturbation theory, that lattice vector gauge theories with Ginsparg Wilson fermions are renormalizable. For two or more massless fermions, they satisfy a flavour mixing axial vector Ward identity. It involves a lattice specific part that is quadratic in the vertex functional and classically irrelevant. We show that it stays irrelevant under renormalization. This means that in the continuum limit the (standard) chiral symmetry becomes restored. In particular, the flavour mixing current does not require renormalization.Comment: 13 pages, Latex2

Linked Cluster Expansions on non-trivial topologies

Linked cluster expansions provide a useful tool both for analytical and numerical investigations of lattice field theories. The expansion parameter is the interaction strength fields at neighboured lattice sites are coupled. They result into convergent series for free energies, correlation functions and susceptibilities. The expansions have been generalized to field theories at finite temperature and to a finite volume. Detailed information on critical behaviour can be extracted from the high order behaviour of the susceptibility series. We outline some of the steps by which the 20th order is achieved.Comment: 3 pages, Talk presented at LATTICE96(Theoretical Developments

Lattice QED and Universality of the Axial Anomaly

We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of species doubling. They hold for Wilson fermions as well as for realizations of the Dirac operator that satisfy the Ginsparg-Wilson relation. The proof is based on the lattice power counting theorem. The results generalize to non-abelian gauge theories.Comment: LATTICE99(theoretical developments) 3 page

A simple construction of fermion measure term in U(1) chiral lattice gauge theories with exact gauge invariance

In the gauge invariant formulation of U(1) chiral lattice gauge theories based on the Ginsparg-Wilson relation, the gauge field dependence of the fermion measure is determined through the so-called measure term. We derive a closed formula of the measure term on the finite volume lattice. The Wilson line degrees of freedom (torons) of the link field are treated separately to take care of the global integrability. The local counter term is explicitly constructed with the local current associated with the cohomologically trivial part of the gauge anomaly in a finite volume. The resulted formula is very close to the known expression of the measure term in the infinite volume with a single parameter integration, and would be useful in practical implementations.Comment: 25 pages, uses JHEP3.cls, the version to appear in JHE

Spectrum of the Hermitian Wilson-Dirac Operator for a Uniform Magnetic Field in Two Dimensions

It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An explicit formula for the secular equations is given in term of a set of polynomials. The spectrum exhibits a fractal structure in the infinite volume limit. An exact result concerning the index theorem for the overlap Dirac operator is obtained.Comment: 8 pages, latex, 3 eps figures, minor correction

Computation of the one-loop Symanzik coefficients for the square action

We compute the one-loop coefficients for an alternative Symanzik improved pure gauge SU{N} lattice action (N=2 and N=3). For the standard Symanzik improved action we confirm previous results by L\"{u}scher and Weisz.Comment: 45 pages, LaTeX, includes library.ps for generating Feynman diagram