153 research outputs found

    Canonical Quantization of Two Dimensional Gauge Fields

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    SU(N)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 AőľA_\mu (in the Cartan subalgebra \h) is quantized. The compact route, as in lattice gauge theory, quantizes the Wilson loop WW, projecting out gauge invariant wavefunctions on the group manifold GG. After a Casimir energy related to the curvature of SU(N)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 GG, Ōá0(W)\chi_0(W), is the first excited state ő®1(Aőľ)\Psi_1(A_\mu) on \h. The ground state ő®0(Aőľ)\Psi_0(A_\mu) does not appear in the character spectrum as its lift is not globally defined on GG. 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

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    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 őĪőľ(f)\alpha^{(f)}_\mu responsible for producing főľőĹCartanf^{\rm Cartan}_{\mu\nu}, the pure gauge part, lattice artifacts, and zero modes. The gauge transformation to the physical gauge field őĪőľ(f)\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

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    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)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

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    %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)SU(N) on S1√óS^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

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    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

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    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 ‚ąľms/10) and at three lattice spacings (a ‚Čą 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

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    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?

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    We examine the question of how baryogenesis can occur in lattice models of the Standard Model where there is a global U(1)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

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    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(182(8) MeV)^4 and an instanton size ‚ąľ0.6\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>TcT > T_c.Comment: 3 pages, 3 PostScript figures (one in color); Talk presented at LAT9
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