Nonlinear Brownian Motion and Higgs Mechanism

TL;DR

This paper extends stochastic quantization with nonlinear terms inspired by active Brownian motion, leading to a natural emergence of the Higgs mechanism's symmetry breaking potential in quantum field theory.

Contribution

It introduces a nonlinear extension to stochastic quantization, connecting active Brownian motion to quantum field theory and deriving the Higgs potential as an equilibrium distribution.

Findings

Equilibrium distributions can be calculated exactly.

The Higgs symmetry breaking potential emerges naturally.

Extension applies to scalar QED.

Abstract

An extension of the stochastic quantization scheme is proposed by adding nonlinear terms to the field equations. Our modification is motivated by the recently established theory of active Brownian motion. We discuss a way of promoting this theory to the case of infinite degrees of freedom. Equilibrium distributions can be calculated exactly and are interpreted as path integral densities of quantum field theories. By applying our procedure to scalar QED, the symmetry breaking potential of the Higgs mechanism arises as the equilibrium solution.