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The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition

Abstract

We study gauge fixing via the standard local extremization algorithm for 2-dimensional U(1). On a lattice with spherical topology S{sup 2} 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. ((orig.)).
Authors:
Forcrand, P de; [1]  Hetrick, J E [2] 
  1. Eidgenoessische Technische Hochschule, Zurich (Switzerland). Interdisciplinary Project Center for Supercomputing
  2. Physics Dept., University of Arizona, Tucson, AZ 85721 (United States)
Publication Date:
Apr 01, 1995
Product Type:
Journal Article
Report Number:
CONF-9409269-
Reference Number:
SCA: 662110; 662230; PA: AIX-26:064340; EDB-95:132537; SN: 95001458356
Resource Relation:
Journal Name: Nuclear Physics B, Proceedings Supplements; Journal Volume: 42; Conference: Lattice `94, Bielefeld (Germany), 25 Sep - 1 Oct 1994; Other Information: PBD: Apr 1995
Subject:
66 PHYSICS; LATTICE FIELD THEORY; ASYMPTOTIC SOLUTIONS; QUANTUM ELECTRODYNAMICS; UNIFIED GAUGE MODELS; ALGORITHMS; CORRELATION FUNCTIONS; EXTREME-VALUE PROBLEMS; FOURIER TRANSFORMATION; GAUGE INVARIANCE; GLOBAL ANALYSIS; LOCALITY; SU-2 GROUPS; TOPOLOGY; TWO-DIMENSIONAL CALCULATIONS; U-1 GROUPS; VECTOR FIELDS; VORTICES
OSTI ID:
101032
Country of Origin:
Netherlands
Language:
English
Other Identifying Numbers:
Journal ID: NPBSE7; ISSN 0920-5632; TRN: NL95FF376064340
Submitting Site:
NLN
Size:
pp. 861-866
Announcement Date:
Oct 05, 1995

Citation Formats

Forcrand, P de, and Hetrick, J E. The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition. Netherlands: N. p., 1995. Web. doi:10.1016/0920-5632(95)00404-W.
Forcrand, P de, & Hetrick, J E. The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition. Netherlands. doi:10.1016/0920-5632(95)00404-W.
Forcrand, P de, and Hetrick, J E. 1995. "The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition." Netherlands. doi:10.1016/0920-5632(95)00404-W. https://www.osti.gov/servlets/purl/10.1016/0920-5632(95)00404-W.
@misc{etde_101032,
title = {The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition}
author = {Forcrand, P de, and Hetrick, J E}
abstractNote = {We study gauge fixing via the standard local extremization algorithm for 2-dimensional U(1). On a lattice with spherical topology S{sup 2} 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. ((orig.)).}
doi = {10.1016/0920-5632(95)00404-W}
journal = {Nuclear Physics B, Proceedings Supplements}
volume = {42}
journal type = {AC}
place = {Netherlands}
year = {1995}
month = {Apr}
}