Hamiltonian Formulations of Yang-Mills Quantum Theory and the Gribov Problem

TL;DR

This paper reviews Hamiltonian approaches to quantizing non-abelian gauge theories, addressing the Gribov problem and comparing instant and front form dynamics in finite volume settings.

Contribution

It provides a comparative analysis of Hamiltonian formulations and gauge fixing methods, highlighting the impact of the Gribov problem in finite volume quantization.

Findings

Analysis of gauge fixing and Gribov issues in finite volume

Comparison of instant and front form quantization methods

Discussion of gauge invariant configuration space

Abstract

We review the status of quantising (non-abelian) gauge theories using different versions of a Hamiltonian formulation corresponding to Dirac's instant and front form of dynamics, respectively. In order to control infrared divergences we work in a finite spatial volume, chosing a torus geometry for convenience. We focus on the determination of the physical configuration space of gauge invariant variables via gauge fixing. This naturally leads us to the issue of the Gribov problem. We discuss it for different gauge choices, in particular finite volume modifications of the axial gauge. Conventional and light-front quantisation are compared and the differences pointed out.