7,910 research outputs found
Gribov Copy and Complex Phase of Chiral Determinant
We calculate the complex phase of chiral determinant by the vacuum overlap
formula with configurations of two-dimensional U(1) gauge field fixed in Landau
and Laplacian gauge. The complex phase fluctuates over the Gribov copies, which
appear in the process of Landau gauge fixing and contain vortex-like
singularities. In the Laplacian gauge, the fluctuation can be reduced and the
phase can be determined uniquely. If it is used as a preconditioning for Landau
gauge fixing, the most smooth configuration is obtained among the copies
generated.Comment: Talk presented at LATTICE96(chiral gauge), 3 LaTeX pages with 5
postscript figures, need espcrc2.sty(included
Symmetry and Symmetry Restoration of Lattice Chiral Fermion in the Overlap Formalism
Three aspects of symmetry structure of lattice chiral fermion in the overlap
formalism are discussed. By the weak coupling expansion of the overlap Dirac
operator, the axial anomaly associated to the chiral transformation proposed by
Luescher is evaluated and is shown to have the correct form of the topological
charge density for perturbative backgrounds. Next we discuss the exponential
suppression of the self-energy correction of the lightest mode in the
domain-wall fermion/truncated overlap. Finally, we consider a supersymmetric
extension of the overlap formula in the case of the chiral multiplet and
examine the symmetry structure of the action.Comment: LATTICE98(chiral), 3 pages, LaTeX using espcrc2.st
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
Chiral Symmetry Restoration in the Schwinger Model with Domain Wall Fermions
Domain Wall Fermions utilize an extra space time dimension to provide a
method for restoring the regularization induced chiral symmetry breaking in
lattice vector gauge theories even at finite lattice spacing. The breaking is
restored at an exponential rate as the size of the extra dimension increases.
Before this method can be used in dynamical simulations of lattice QCD, the
dependence of the restoration rate to the other parameters of the theory and,
in particular, the lattice spacing must be investigated. In this paper such an
investigation is carried out in the context of the two flavor lattice Schwinger
model.Comment: LaTeX, 37 pages including 18 figures. Added comments regarding power
law fitting in sect 7. Also, few changes were made to elucidate the content
in sect. 5.1 and 5.3. To appear in Phys. Rev.
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
On the continuum limit of fermionic topological charge in lattice gauge theory
It is proved that the fermionic topological charge of SU(N) lattice gauge
fields on the 4-torus, given in terms of a spectral flow of the Hermitian
Wilson--Dirac operator, or equivalently, as the index of the Overlap Dirac
operator, reduces to the continuum topological charge in the classical
continuum limit when the parameter is in the physical region .Comment: latex, 18 pages. v2: Several comments added. To appear in J.Math.Phy
Ginsparg-Wilson Fermions: A study in the Schwinger Model
Qualitative features of Ginsparg-Wilson fermions, as formulated by Neuberger,
coupled to two dimensional U(1) gauge theory are studied. The role of the
Wilson mass parameter in changing the number of massless flavors in the theory
and its connection with the index of the Dirac operator is studied. Although
the index of the Dirac operator is not related to the geometric definition of
the topological charge for strong couplings, the two start to agree as soon as
one goes to moderately weak couplings. This produces the desired singularity in
the quenched chiral condensate which appears to be very difficult to reproduce
with staggered fermions. The fermion determinant removes the singularity and
reproduces the known chiral condensate and the meson mass within understandable
errors.Comment: Corrected a few typos and changed some references. Minor changes to
the conten
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
Dynamical QCD thermodynamics with domain wall fermions
We present results from numerical simulations of full, two flavor QCD
thermodynamics at N_t=4 with domain wall fermions. For the first time a
numerical simulation of the full QCD phase transition displays a low
temperature phase with spontaneous chiral symmetry breaking but intact flavor
symmetry and a high temperature phase with the full SU(2) x SU(2) chiral flavor
symmetry.Comment: LATTICE98(hightemp
The staggered domain wall fermion method
A different lattice fermion method is introduced. Staggered domain wall
fermions are defined in 2n+1 dimensions and describe 2^n flavors of light
lattice fermions with exact U(1) x U(1) chiral symmetry in 2n dimensions. As
the size of the extra dimension becomes large, 2^n chiral flavors with the same
chiral charge are expected to be localized on each boundary and the full
SU(2^n) x SU(2^n) flavor chiral symmetry is expected to be recovered. SDWF give
a different perspective into the inherent flavor mixing of lattice fermions and
by design present an advantage for numerical simulations of lattice QCD
thermodynamics. The chiral and topological index properties of the SDWF Dirac
operator are investigated. And, there is a surprise ending...Comment: revtex4, 7 figures, minor revisions, 2 references adde
- …