Gauge independence of the physical fermion mass in the effective action of theories with radiative symmetry breaking

TL;DR

This paper demonstrates that in an Abelian gauge theory with radiative symmetry breaking, the physical fermion mass remains gauge-independent, confirmed through derivation and verification of Nielsen identities.

Contribution

It derives and verifies Nielsen identities ensuring gauge independence of the physical fermion mass in theories with radiative symmetry breaking.

Findings

Gauge independence of the fermion mass is confirmed.

Nielsen identities are derived and verified.

Effective action analysis supports gauge-invariant physical predictions.

Abstract

I consider an Abelian gauge theory, with a complex scalar field and massless, chiral fermions, in the limit where the couplings and the interactions induce radiative symmetry breaking, and I derive and verify the Nielsen identities that ensure the gauge independence of the physical fermion mass that emerges in the broken phase of the effective action.