On Gauge Invariance and Spontaneous Symmetry Breaking

TL;DR

This paper explains spontaneous symmetry breaking within causal perturbation theory using a perturbative gauge invariance framework, focusing on Abelian gauge theories with implications for electroweak theory.

Contribution

It introduces a perturbative approach to gauge invariance that clarifies spontaneous symmetry breaking in quantum gauge theories.

Findings

Perturbative gauge invariance can be formulated using asymptotic fields.

The approach is demonstrated in Abelian U(1) gauge theory.

Relevance to electroweak theory is discussed.

Abstract

We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.