Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1994-12-08
Nucl.Phys.Proc.Suppl. 42 (1995) 861-866
Physics
High Energy Physics
High Energy Physics - Lattice
6 pages, uuencoded postscript, presented at Lattice 94
Scientific paper
10.1016/0920-5632(95)00404-W
We study gauge fixing via the standard local extremization algorithm for 2-dimensional $U(1)$. On a lattice with spherical topology $S^2$ 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.
Forcrand Philippe de
Hetrick James E.
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