2,246 research outputs found
Exact Chiral Symmetry on the Lattice
Developments during the last eight years have refuted the folklore that
chiral symmetries cannot be preserved on the lattice. The mechanism that
permits chiral symmetry to coexist with the lattice is quite general and may
work in Nature as well. The reconciliation between chiral symmetry and the
lattice is likely to revolutionize the field of numerical QCD.Comment: 30 pages, LaTeX, reference adde
Remark on lattice BRST invariance
A recently claimed resolution to the lattice Gribov problem in the context of
chiral lattice gauge theories is examined. Unfortunately, I find that the old
problem remains.Comment: 4 pages, plain TeX, presentation improved (see acknowledgments
Exact results and approximation schemes for the Schwinger model with the overlap Dirac operator
We propose new techniques to implement numerically the overlap-Dirac operator
which exploit the physical properties of the underlying theory to avoid nested
algorithms. We test these procedures in the two-dimensional Schwinger model and
the results are very promising. We also present a detailed computation of the
spectrum and chiral properties of the Schwinger Model in the overlap lattice
formulation.Comment: Lattice 2000 (Chiral Fermions
Considerations on Neuberger's operator
We discuss new approaches to the numerical implementation of Neuberger's
operator for lattice fermions and the possible use of block spin
transformations.Comment: LATTICE 99 (Improvement and Renormalization
Proposal for the numerical solution of planar QCD
Using quenched reduction, we propose a method for the numerical calculation
of meson correlation functions in the planar limit of QCD. General features of
the approach are outlined, and an example is given in the context of
two-dimensional QCD.Comment: 31 pages, 10 figures, uses axodraw.sty, To appear in Physical Review
Two dimensional fermions in three dimensional YM
Dirac fermions in the fundamental representation of SU(N) live on the surface
of a cylinder embedded in and interact with a three dimensional SU(N)
Yang Mills vector potential preserving a global chiral symmetry at finite .
As the circumference of the cylinder is varied from small to large, the chiral
symmetry gets spontaneously broken in the infinite limit at a typical bulk
scale. Replacing three dimensional YM by four dimensional YM introduces
non-trivial renormalization effects.Comment: 21 pages, 7 figures, 5 table
The Problem on the Lattice
If the expression of the topological charge density operator, suggested by
fermions obeying the Ginsparg--Wilson relation, is employed, it is possible to
prove on the lattice the validity of the Witten--Veneziano formula for the
mass. Recent numerical results from simulations with overlap fermions
in 2 (abelian Schwinger model) and 4 (QCD) dimensions give values for the mass
of the lightest pseudo-scalar flavour-singlet state that agree with theoretical
expectations and/or experimental data.Comment: 3 pages, talk presented by G.C. Rossi at Lattice2001(theorydevelop
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
One loop calculation in lattice QCD with domain-wall quarks
One loop corrections to the domain-wall quark propagator are calculated in
massless QCD. It is shown that no additative counter term to the current quark
mass is generated in this theory, and the wave function renormalization factor
of the massless quark is explicitly evaluated. We also show that an analysis
with a simple mean-field approximation can explain properties of the massless
quark in numerical simulations of QCD with domain-wall quarks.Comment: 24 pages, REVTeX, with 3 epsf figure
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