QCD, Gauge Fixing, and the Gribov Problem
A.G. Williams
TL;DR
This paper discusses the limitations of standard gauge-fixing methods in nonperturbative QCD due to Gribov copies and explores implications of non-local gauge fixing on theoretical properties.
Contribution
It analyzes the impact of Gribov copies on gauge fixing in nonperturbative QCD and examines non-local gauges like Laplacian gauge.
Findings
Standard gauge fixing fails nonperturbatively due to Gribov copies.
Non-local gauges can eliminate Gribov copies but affect BRST invariance.
Implications for ghost fields and renormalizability are discussed.
Abstract
The standard techniques of gauge-fixing, such as covariant gauge fixing, are entirely adequate for the purposes of studies of perturbative QCD. However, they fail in the nonperturbative regime due to the presence of Gribov copies. These copies arise because standard local gauge fixing methods do not completely fix the gauge. Known Gribov-copy-free gauges, such as Laplacian gauge, are manifestly non-local. These issues are examined and the implications of non-local gauge-fixing for ghost fields, BRST invariance, and the proof of renormalizability of QCD are considered.
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