The Metric of Yang-Mills Orbit Space on the Lattice
M. Laufer (Graduate Center, CUNY), P. Orland (Baruch College and, Grad Center, CUNY)
TL;DR
This paper derives the metric, inverse metric, and Laplace-Beltrami operator for the orbit space of SU(2) gauge theory on a lattice, providing a complete gauge fixing that resolves the Gribov problem.
Contribution
It introduces a comprehensive coordinate system and metric for the lattice gauge orbit space, fully solving the Gribov ambiguity in axial gauge.
Findings
Explicit metric tensor and inverse for SU(2) orbit space
Complete gauge fixing eliminates Gribov ambiguities
Lays groundwork for spectral analysis of lattice gauge theories
Abstract
We find coordinates, the metric tensor, the inverse metric tensor and the Laplace-Beltrami operator for the orbit space of Hamiltonian SU(2) gauge theory on a finite, rectangular lattice. This is done using a complete axial gauge fixing. The Gribov problem can be completely solved, with no remaining gauge ambiguities.
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