8 research outputs found
A lattice path integral for supersymmetric quantum mechanics
We report on a study of the supersymmetric anharmonic oscillator computed
using a euclidean lattice path integral. Our numerical work utilizes a Fourier
accelerated hybrid Monte Carlo scheme to sample the path integral. Using this
we are able to measure massgaps and check Ward identities to a precision of
better than one percent. We work with a non-standard lattice action which we
show has an {\it exact} supersymmetry for arbitrary lattice spacing in the
limit of zero interaction coupling. For the interacting model we show that
supersymmetry is restored in the continuum limit without fine tuning. This is
contrasted with the situation in which a `standard' lattice action is employed.
In this case supersymmetry is not restored even in the limit of zero lattice
spacing. Finally, we show how a minor modification of our action leads to an
{\it exact}, local lattice supersymmetry even in the presence of interaction.Comment: 18 pages, 7 figures, 1 reference added, 1 correcte
Application of Maximum Entropy Method to Lattice Field Theory with a Topological Term
In Monte Carlo simulation, lattice field theory with a term suffers
from the sign problem.
This problem can be circumvented by Fourier-transforming the topological
charge distribution . Although this strategy works well for small lattice
volume, effect of errors of
becomes serious with increasing volume and prevents one from studying
the phase structure. This is called flattening. As an alternative approach, we
apply the maximum entropy method (MEM) to the Gaussian . It is found that
the flattening could be much improved by use of the MEM.Comment: talk at Lattice 2003 (topology), 3 pages with 3 figure
New possibilities for QCD at finite density
I review the growing theoretical indications that at high densities color
SU(3) gauge symmetry is spontaneously broken by the formation of a quark pair
condensate. This leads to a rich phase structure for QCD as a function of
temperature and chemical potential.
I also discuss the prospects for lattice QCD calculations at finite density,
including the Glasgow algorithm and imaginary chemical potential.Comment: LATTICE98(hightemp), 6 pages, LaTe
Locality Properties of a New Class of Lattice Dirac Operators
A new class of lattice Dirac operators which satisfy the index theorem
have been recently proposed on the basis of the algebraic relation
. Here stands for a non-negative integer and
corresponds to the ordinary Ginsparg-Wilson relation. We analyze the
locality properties of Dirac operators which solve the above algebraic
relation.
We first show that the free fermion operator is analytic in the entire
Brillouin zone for a suitable choice of parameters and , and there
exists a well-defined ``mass gap'' in momentum space, which in turn leads to
the exponential decay of the operator in coordinate space for any finite .
This mass gap in the free fermion operator suggests that the operator is local
for sufficiently weak background gauge fields. We in fact establish a finite
locality domain of gauge field strength for
for any finite , which is
sufficient for the cohomological analyses of chiral gauge theory. We also
present a crude estimate of the localization length defined by an exponential
decay of the Dirac operator, which turns out to be much shorter than the one
given by the general Legendre expansion.Comment: Some clarifying comments are added, and a misprint was corrected.
Nuclear Physics B(in press
Exact chiral symmetry, topological charge and related topics
It has been shown recently that Dirac operators satisfying the
Ginsparg-Wilson relation provide a solution of the chirality problem in QCD at
finite lattice spacing. We discuss different ways to construct these operators
and their properties. The possibility to define lattice chiral gauge theories
is briefly discussed as well.Comment: 15 pages, latex, 3 figures, LATTICE98, plenary tal
Lattice Chiral Fermions
I review the ongoing attempts to define chiral gauge theories using the
lattice regularization.Comment: Plenary talk at Lattice'95, Melbourne, Australia. LaTeX, 16 page