Nonlinear Phenomena in Canonical Stochastic Quantization

TL;DR

This paper explores nonlinear phenomena in stochastic quantization, particularly using nonlinear Brownian motion, and introduces a new formulation of the Higgs mechanism within quantum electrodynamics, linking quantum field theory and statistical mechanics.

Contribution

It presents a novel approach to stochastic quantization involving nonlinear Brownian motion and proposes a new formulation of the Higgs mechanism in QED.

Findings

Nonlinear phenomena emerge in stochastic quantization with nonlinear Brownian motion.

A new formulation of the Higgs mechanism in QED is proposed.

The work connects quantum field theory with statistical mechanics through nonlinear stochastic processes.

Abstract

Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochastic process. We discuss a novel formulation of the Higgs mechanism in QED.