Coulomb gauge Green functions and Gribov copies in SU(2) lattice gauge theory

TL;DR

This study investigates Coulomb gauge Green functions in SU(2) lattice gauge theory, revealing significant effects of Gribov copies especially at low momenta, and improving agreement with continuum Hamiltonian calculations.

Contribution

It introduces an improved gauge fixing scheme and provides new insights into the impact of Gribov copies on Green functions in lattice gauge theory.

Findings

Green functions are more affected by Gribov copies than previously thought.

Infra-red lattice results align better with continuum Hamiltonian approaches.

Low-momentum Green functions show significant influence from gauge fixing ambiguities.

Abstract

We reconsider the lattice measurement of Green functions in Coulomb gauge, both in 2+1 and 3+1 dimensions, using an improved gauge fixing scheme. The influence of Gribov copies is examined and we find clear indications that Green functions are more strongly affected than previously assumed, in particular for low momenta. Qualitatively, our improved lattice results in the infra-red compare more favourably with recent continuum calculations in the Hamiltonian approach.