Nonperturbative Stochastic Quantization of the Helix Model

TL;DR

This paper develops a nonperturbative stochastic quantization method for the helix model, a gauge theory in 0+1 dimensions, establishing its equivalence with the path integral approach and introducing a geometric gauge fixing technique.

Contribution

It introduces a geometrical approach to stochastic gauge fixing and proves nonperturbative equivalence with the path integral formalism for the helix model.

Findings

Successful nonperturbative quantization of the helix model

Development of a generalized stochastic gauge fixing procedure

Demonstration of equivalence with path integral formalism

Abstract

The helix model describes the minimal coupling of an abelian gauge field with three bosonic matter fields in 0+1 dimensions; it is a model without a global Gribov obstruction. We perform the stochastic quantization in configuration space and prove nonperturbatively equivalence with the path integral formalism. Major points of our approach are the geometrical understanding of separations into gauge independent and gauge dependent degrees of freedom as well as a generalization of the stochastic gauge fixing procedure which allows to extract the equilibrium Fokker-Planck probability distribution of the model.