2,422 research outputs found
The overlap lattice Dirac operator and dynamical fermions
I show how to avoid a two level nested conjugate gradient procedure in the
context of Hybrid Monte Carlo with the overlap fermionic action. The resulting
procedure is quite similar to Hybrid Monte Carlo with domain wall fermions, but
is more flexible and therefore has some potential worth exploring.Comment: Further expanded version. 12 pages, plain Te
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
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
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
Improving the low-lying spectrum of the overlap kernel
The action of the overlap-Dirac operator on a vector is typically implemented
in directly through a multi-shift conjugate gradient solver. The compute-time
this takes to evaluate depends upon the condition number of the matrix
that is used as the overlap kernel. We examine the low-lying spectra of various
candidate kernels in an effort to optimise , thereby speeding up the
overlap evaluation.Comment: 5 pages, 8 figure
Nonperturbative Gauge Fixing and Perturbation Theory
We compare the gauge-fixing approach proposed by Jona-Lasinio and Parrinello,
and by Zwanziger (JPLZ) with the standard Fadeev-Popov procedure, and
demonstrate perturbative equality of gauge-invariant quantities, up to
irrelevant terms induced by the cutoff. We also show how a set of local,
renormalizable Feynman rules can be constructed for the JPLZ procedure.Comment: 9 pages, latex, version to appear in Phys. Rev.
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
A practical implementation of the Overlap-Dirac operator
A practical implementation of the Overlap-Dirac operator
is presented. The implementation exploits
the sparseness of and does not require full storage. A simple application
to parity invariant three dimensional SU(2) gauge theory is carried out to
establish that zero modes related to topology are exactly reproduced on the
lattice.Comment: Y-axis label in figure correcte
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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