123 research outputs found
Canonical Quantization of Two Dimensional Gauge Fields
gauge fields on a cylindrical spacetime are canonically quantized via
two routes revealing almost equivalent but different quantizations. After
removing all continuous gauge degrees of freedom, the canonical coordinate
(in the Cartan subalgebra \h) is quantized. The compact route, as in
lattice gauge theory, quantizes the Wilson loop , projecting out gauge
invariant wavefunctions on the group manifold . After a Casimir energy
related to the curvature of is added to the compact spectrum, it is
seen to be a subset of the non-compact spectrum. States of the two
quantizations with corresponding energy are shifted relative each other, such
that the ground state on , , is the first excited state
on \h. The ground state does not appear in
the character spectrum as its lift is not globally defined on . Implications
for lattice gauge theory and the sum over maps representation of two
dimensional QCD are discussed.Comment: 32 pages, 3 figures uuencoded, Plain Te
Hodge gauge fixing in three dimensions
A progress report on experiences with a gauge fixing method proposed in
LATTICE 94 is presented. In this algorithm, an SU(N) operator is diagonalized
at each site, followed by gauge fixing the diagonal (Cartan) part of the links
to Coulomb gauge using the residual abelian freedom. The Cartan sector of the
link field is separated into the physical gauge field
responsible for producing , the pure gauge part,
lattice artifacts, and zero modes. The gauge transformation to the physical
gauge field is then constructed and performed. Compactness
of the lattice fields entails issues related to monopoles and zero modes which
are addressed.Comment: 4 pages Latex, 3 postscript figures, Poster presented at
LATTICE96(topology
Some Non-Perturbative Aspects of Gauge Fixing in Two Dimensional Yang-Mills Theory
Gauge fixing in general is incomplete, such that one solves some of the gauge
constraints, quantizes, then imposes any residual gauge symmetries (Gribov
copies) on the wavefunctions. While the Fadeev-Popov determinant keeps track of
the local metric on this gauge fixed surface, the global topology of the
reduced configuration space can be different depending on the treatment of the
residual symmetries, which can in turn affect global properties of the theory
such as the vacuum wavefunction. Pure gauge theory in two dimensions
provides a simple yet non-trivial example where the above structure and effects
can be elucidated explicitly, thus displaying physical effects of the treatment
of Gribov copies.Comment: 3 pages (14.2kb), LaTeX + uufiles: 1 PS figure and sty file, Talk
presented at LATTICE 93, ITFA-93-3
Gauge fixing and Gribov copies in pure Yang-Mills on a circle
%In order to understand how gauge fixing can be affected on the %lattice, we
first study a simple model of pure Yang-mills theory on a %cylindrical
spacetime [ on {\bf R}] where the %gauge fixed subspace is
explicitly displayed. On the way, we find that %different gauge fixing
procedures lead to different Hamiltonians and %spectra, which however coincide
under a shift of states. The lattice %version of the model is compared and
lattice gauge fixing issues are %discussed. (---TALK GIVEN AT LATTICE
92---AMSTERDAM, 15 SEPT. 92)Comment: 4 pages + 1 PostScript figure (appended),
UVA-ITFA-92-34/ETH-IPS-92-22. --just archiving published versio
B- and D-meson decay constants from three-flavor lattice QCD
We calculate the leptonic decay constants of B(s) and D(s) mesons in lattice QCD using staggered light quarks and Fermilab bottom and charm quarks. We compute the heavy-light-meson correlation functions on the MILC Asqtad-improved staggered gauge configurations, which include the effects of three light dynamical sea quarks. We simulate with several values of the light valence- and sea-quark masses (down to ∼ms/10) and at three lattice spacings (a ≈ 0.15, 0.12, and 0.09 fm) and extrapolate to the physical up and down quark masses and the continuum using expressions derived in heavy-light-meson staggered chiral perturbation theory. We renormalize the heavy-light axial current using a mostly nonperturbative method such that only a small correction to unity must be computed in lattice perturbation theory, and higher-order terms are expected to be small. We use the two finer lattice spacings for our central analysis, and we use the third to help estimate discretization errors. We obtain fB + = 196.9 (9.1) MeV, fBs = 242.0 (10.0) MeV, fD + = 218.9 (11.3) MeV, fDs = 260.1 (10.8) MeV, and the SU(3) flavor-breaking ratios fBs /fB =1.229 (26) and fDs/fD = 1.188 (25), where the numbers in parentheses are the total statistical and systematic uncertainties added in quadrature
Topological Properties of the QCD Vacuum at T=0 and T ~ T_c
We study on the lattice the topology of SU(2) and SU(3) Yang-Mills theories
at zero temperature and of QCD at temperatures around the phase transition. To
smooth out dislocations and the UV noise we cool the configurations with an
action which has scale invariant instanton solutions for instanton size above
about 2.3 lattice spacings. The corresponding "improved" topological charge
stabilizes at an integer value after few cooling sweeps. At zero temperature
the susceptibility calculated from this charge (about (195MeV)^4 for SU(2) and
(185 MeV)^4 for SU(3)) agrees very well with the phenomenological expectation.
At the minimal amount of cooling necessary to resolve the structure in terms of
instantons and anti-instantons we observe a dense ensemble where the total
number of peaks is by a factor 5-10 larger than the net charge. The average
size observed for these peaks at zero temperature is about 0.4-0.45 fm for
SU(2) and 0.5-0.6 fm for SU(3). The size distribution changes very little with
further cooling, although in this process up to 90% of the peaks disappear by
pair annihilation. For QCD we observe below T_c a reduction of the topological
susceptibility as an effect of the dynamical fermions. Nevertheless also here
the instantons form a dense ensemble with general characteristics similar to
those of the quenched theory. A further drop in the susceptibility above T_c is
also in rough agreement with what has been observed for pure SU(3). We see no
clear signal for dominant formation of instanton - anti-instanton molecules.Comment: Latex, 7 pages, 4 figures (one colour). Contribution to the 31st
International Symposium Ahrenshoop on the Theory of Elementary Particles,
Buckow, September 2-6, 199
The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition
We study gauge fixing via the standard local extremization algorithm for
2-dimensional . On a lattice with spherical topology where all
copies are lattice artifacts, we find that the number of these 'Gribov' copies
diverges in the continuum limit. On a torus, we show that lattice artifacts can
lead to the wrong evaluation of the gauge-invariant correlation length, when
measured via a gauge-fixed procedure; this bias does not disappear in the
continuum limit. We then present a new global approach, based on Hodge
decomposition of the gauge field, which produces a unique smooth field in
Landau gauge, and is economically powered by the FFT. We also discuss the use
of this method for examining topological objects, and its extensions to
non-abelian gauge fields.Comment: 6 pages, uuencoded postscript, presented at Lattice 9
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