153 research outputs found

### Canonical Quantization of Two Dimensional Gauge Fields

$SU(N)$ 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
$A_\mu$ (in the Cartan subalgebra \h) is quantized. The compact route, as in
lattice gauge theory, quantizes the Wilson loop $W$, projecting out gauge
invariant wavefunctions on the group manifold $G$. After a Casimir energy
related to the curvature of $SU(N)$ 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 $G$, $\chi_0(W)$, is the first excited state
$\Psi_1(A_\mu)$ on \h. The ground state $\Psi_0(A_\mu)$ does not appear in
the character spectrum as its lift is not globally defined on $G$. 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 $\alpha^{(f)}_\mu$
responsible for producing $f^{\rm Cartan}_{\mu\nu}$, the pure gauge part,
lattice artifacts, and zero modes. The gauge transformation to the physical
gauge field $\alpha^{(f)}_\mu$ 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 $SU(N)$ 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 [$SU(N)$ on $S^1 \times$ {\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

### Fermion Number Conservation Isn't Fermion Conservation

A nonperturbative regularization of the Standard Model may have a
superficially undesirable exact global U(1) symmetry corresponding to exact
fermion number conservation. We argue that such a formulation can still have
the desired physics of fermion nonconservation, i.e. fermion particle creation
and annihilation by sphaleron transitions. We illustrate our reasoning in
massless axial QED in 1+1 dimensions.Comment: 3 pages to appear in the proceedings of Lattice '93, Dallas, Texas,
12-16 October 1993, comes as a single uuencoded postscript file (LaTeX source
available from the authors), ITFA 93-3

### 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

### Can baryogenesis occur on the lattice?

We examine the question of how baryogenesis can occur in lattice models of
the Standard Model where there is a global $U(1)$ symmetry which is accompanied
by an exactly conserved fermion number. We demonstrate that fermion creation
and annihilation can occur in these models {\em despite} this exact fermion
number conservation, by explicitly computing the spectral flow of the
hamiltonian in the two dimensional U(1) axial model with Wilson fermions. For
comparison we also study the closely related Schwinger model where a similar
mechanism gives rise to anomalous particle creation and annihilation.Comment: 5 pp., contribution to the conference "Trends in Astroparticle
Physics", Stockholm, 2 ps figs. (uuencoded

### Topology of full QCD

We study topological properties of SU(3) gauge theory using improved cooling.
In the absence of fermions, we measure a topological susceptibility of $(182(8)
MeV)^4$ and an instanton size $\sim 0.6$ fm. In the presence of light staggered
fermions and across the chiral transition, the susceptibility drops in a manner
consistent with the quenched case, and the instanton size changes little. No
significant formation of bound instanton-antiinstanton pairs is observed, in
particular not along the Euclidean time direction for $T > T_c$.Comment: 3 pages, 3 PostScript figures (one in color); Talk presented at LAT9

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