Ward-Takahashi Identity and Dynamical Mass Generation in Abelian Gauge Theories

TL;DR

This paper develops a method using Ward-Takahashi identities to analyze dynamical mass generation and symmetry breaking in Abelian gauge theories, providing new insights into composite Higgs and Goldstone boson properties.

Contribution

It introduces a novel approach linking elementary and composite fields to study dynamical symmetry breaking and mass generation in Abelian gauge theories.

Findings

Gauge boson masses agree with existing results.

New predictions for composite Higgs boson mass.

Calculated Goldstone boson decay constant.

Abstract

We derive Ward-Takahashi identities including composite fields in Abelian gauge theories and the matching condition between the elementary field description and the composite field description. With these we develop an approach to dynamical symmetry breaking in Abelian gauge theories including the study of the dynamically generated masses of the gauge boson, the fermions and the composite Higgs field. The Cornwall-Norton, Jackiw-Johnson and Schwinger models are taken as examples of the application. The obtained gauge boson masses are in agreement with the existing results. In this appraoch, we are able to further obtain new results for the mass of the composite Higgs boson and the goldstone boson decay constant.