Generalized Stochastic Quantization of Yang-Mills Theory

TL;DR

This paper develops a generalized stochastic quantization method for Yang-Mills theory, deriving the Faddeev-Popov path integral as an exact equilibrium solution, with a focus on gauge fixing and geometric interpretation.

Contribution

It introduces a generalized stochastic gauge fixing scheme for Yang-Mills theory and provides a rigorous derivation of the Faddeev-Popov path integral as an equilibrium solution.

Findings

Derived the Faddeev-Popov path integral from stochastic quantization.

Established the geometric interpretation of the gauge fixing scheme.

Clarified the validity range of the approach.

Abstract

We perform the stochastic quantization of Yang-Mills theory in configuration space and derive the Faddeev-Popov path integral density. Based on a generalization of the stochastic gauge fixing scheme and its geometrical interpretation this result is obtained as the exact equilibrium solution of the associated Fokker--Planck equation. Included in our discussion is the precise range of validity of our approach.