2,383 research outputs found
A simple derivation of the Overlap Dirac Operator
We derive the vector-like four dimensional overlap Dirac operator starting
from a five dimensional Dirac action in the presence of a delta-function
space-time defect. The effective operator is obtained by first integrating out
all the fermionic modes in the fixed gauge background, and then identifying the
contribution from the localized modes as the determinant of an operator in one
dimension less. We define physically relevant degrees of freedom on the defect
by introducing an auxiliary defect-bound fermion field and integrating out the
original five dimensional bulk field.Comment: 9 pages, LaTe
An alternative to domain wall fermions
We define a sparse hermitian lattice Dirac matrix, , coupling Dirac
fermions. When fermions are integrated out the induced action for the last
fermion is a rational approximation to the hermitian overlap Dirac operator. We
provide rigorous bounds on the condition number of and compare them to
bounds for the higher dimensional Dirac operator of domain wall fermions. Our
main conclusion is that overlap fermions should be taken seriously as a
practical alternative to domain wall fermions in the context of numerical QCD.Comment: Revtex Latex, 26 pages, 1 figure, a few minor change
Bounds on the Wilson Dirac Operator
New exact upper and lower bounds are derived on the spectrum of the square of
the hermitian Wilson Dirac operator. It is hoped that the derivations and the
results will be of help in the search for ways to reduce the cost of
simulations using the overlap Dirac operator. The bounds also apply to the
Wilson Dirac operator in odd dimensions and are therefore relevant to domain
wall fermions as well.Comment: 16 pages, TeX, 3 eps figures, small corrections and improvement
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
Domain Wall Fermions with Exact Chiral Symmetry
We show how the standard domain wall action can be simply modified to allow
arbitrarily exact chiral symmetry at finite fifth dimensional extent. We note
that the method can be used for both quenched and dynamical calculations. We
test the method using smooth and thermalized gauge field configurations. We
also make comparisons of the performance (cost) of the domain wall operator for
spectroscopy compared to other methods such as the overlap-Dirac operator and
find both methods are comparable in cost.Comment: revtex, 37 pages, 11 color postscript figure
Chiral Fermions and Multigrid
Lattice regularization of chiral fermions is an important development of the
theory of elementary particles. Nontheless, brute force computer simulations
are very expensive, if not prohibitive. In this letter I exploit the
non-interacting character of the lattice theory in the flavor space and propose
a multigrid approach for the simulation of the theory. Already a two-grid
algorithm saves an order of magnitude of computer time for fermion propagator
calculations.Comment: Latex, 6 pages, 1 figur
Finite size effects on in QCD from Chiral Perturbation Theory
We present a determination of the shift due to the finite
spatial box size by means of Chiral Perturbation Theory and
L\"uscher's formula. The range of applicability of the chiral prediction is
discussed.Comment: 3 pages, 3 figures, Lattice2002(spectrum
Noncompact chiral U(1) gauge theories on the lattice
A new, adiabatic phase choice is adopted for the overlap in the case of an
infinite volume, noncompact abelian chiral gauge theory. This gauge choice
obeys the same symmetries as the Brillouin-Wigner (BW) phase choice, and, in
addition, produces a Wess-Zumino functional that is linear in the gauge
variables on the lattice. As a result, there are no gauge violations on the
trivial orbit in all theories, consistent and covariant anomalies are simply
related and Berry's curvature now appears as a Schwinger term. The adiabatic
phase choice can be further improved to produce a perfect phase choice, with a
lattice Wess-Zumino functional that is just as simple as the one in continuum.
When perturbative anomalies cancel, gauge invariance in the fermionic sector is
fully restored. The lattice effective action describing an anomalous abelian
gauge theory has an explicit form, close to one analyzed in the past in a
perturbative continuum framework.Comment: 35 pages, one figure, plain TeX; minor typos corrected; to appear in
PR
A study of chiral symmetry in quenched QCD using the Overlap-Dirac operator
We compute fermionic observables relevant to the study of chiral symmetry in
quenched QCD using the Overlap-Dirac operator for a wide range of the fermion
mass. We use analytical results to disentangle the contribution from exact zero
modes and simplify our numerical computations. Details concerning the numerical
implementation of the Overlap-Dirac operator are presented.Comment: 24 pages revtex with 5 postscript figures included by eps
A Study of Practical Implementations of the Overlap-Dirac Operator in Four Dimensions
We study three practical implementations of the Overlap-Dirac operator in four dimensions. Two implementations are
based on different representations of as a sum over poles. One
of them is a polar decomposition and the other is an optimal fit to a ratio of
polynomials. The third one is obtained by representing using
Gegenbauer polynomials and is referred to as the fractional inverse method.
After presenting some spectral properties of the Hermitian operator
, we study its spectrum in a smooth SU(2) instanton
background with the aim of comparing the three implementations of . We
also present some results in SU(2) gauge field backgrounds generated at
on an lattice. Chiral properties have been numerically
verified.Comment: 23 pages latex with 9 postscript figures included by epsf. Some
change in referencing and one figure modifie
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