Quantizing Yang-Mills Theory: From Parisi-Wu Stochastic Quantization to a Global Path Integral

TL;DR

This paper introduces a generalized stochastic quantization approach for Yang-Mills theory, leading to a globally defined Faddeev-Popov path integral that relates to the original Parisi-Wu scheme.

Contribution

It proposes a novel global path integral formulation for Yang-Mills theory based on an extended stochastic quantization method.

Findings

Developed a globally defined Faddeev-Popov path integral density.

Connected the global path integral to the Parisi-Wu stochastic quantization scheme.

Provided a new perspective on gauge potential space and gauge orbit space.

Abstract

Based on a generalization of the stochastic quantization scheme we recently proposed a generalized, globally defined Faddeev-Popov path integral density for the quantization of Yang-Mills theory. In this talk first our approach on the whole space of gauge potentials is shortly reviewed; in the following we discuss the corresponding global path integral on the gauge orbit space relating it to the original Parisi-Wu stochastic quantization scheme.