QED Revisited: Proving Equivalence Between Path Integral and Stochastic Quantization

TL;DR

This paper demonstrates that stochastic quantization of scalar QED, using a generalized gauge fixing scheme, precisely matches the traditional path integral approach, providing a geometric interpretation.

Contribution

It introduces a generalized stochastic gauge fixing scheme and proves its exact equivalence to the path integral formulation for scalar QED.

Findings

Stochastic quantization agrees exactly with path integral formulation.

Provides a geometric interpretation of stochastic gauge fixing.

Validates stochastic quantization as an alternative to path integrals.

Abstract

We perform the stochastic quantization of scalar QED based on a generalization of the stochastic gauge fixing scheme and its geometric interpretation. It is shown that the stochastic quantization scheme exactly agrees with the usual path integral formulation.