Symmetry Breaking in the Schr\"odinger Representation for Chern-Simons Theories

TL;DR

This paper explores spontaneous symmetry breaking in the Schr"odinger representation of 3D abelian gauge theories, analyzing how different gauge terms influence mass generation.

Contribution

It provides a detailed analysis of symmetry breaking phenomena in the Schr"odinger representation for various 3D abelian gauge theories with different gauge actions.

Findings

Symmetry breaking occurs in the Schr"odinger representation for these theories.

Different gauge terms lead to distinct mass generation mechanisms.

The analysis clarifies the role of the Schr"odinger representation in understanding gauge symmetry breaking.

Abstract

This paper discusses the phenomenon of spontaneous symmetry breaking in the Schr\"odinger representation formulation of quantum field theory. The analysis is presented for three-dimensional space-time abelian gauge theories with either Maxwell, Maxwell-Chern-Simons, or pure Chern-Simons terms as the gauge field contribution to the action, each of which leads to a different form of mass generation for the gauge fields.