Global Path Integral Quantization of Yang-Mills Theory

TL;DR

This paper develops a globally consistent path integral formulation for Yang-Mills theory that addresses gauge fixing ambiguities and the Gribov problem, ensuring independence from local gauge choices.

Contribution

It introduces a global path integral density for Yang-Mills theory by summing over gauge patches, overcoming local gauge fixing limitations and relating to stochastic quantization.

Findings

Proposed a gauge patch summation method for global path integrals.

Proved independence of the path integral from local gauge fixing choices.

Connected the global path integral to stochastic quantization and existing proposals.

Abstract

Based on a generalization of the stochastic quantization scheme recently a modified Faddeev-Popov path integral density for the quantization of Yang-Mills theory was derived, the modification consisting in the presence of specific finite contributions of the pure gauge degrees of freedom. Due to the Gribov problem the gauge fixing can be defined only locally and the whole space of gauge potentials has to be partitioned into patches. We propose a global path integral density for the Yang-Mills theory by summing over all patches, which can be proven to be manifestly independent of the specific local choices of patches and gauge fixing conditions, respectively. In addition to the formulation on the whole space of gauge potentials we discuss the corresponding global path integral on the gauge orbit space relating it to the original Parisi-Wu stochastic quantization scheme and to a proposal of Stora, respectively.