Pseudo-Hermitian approach to Goldstone's theorem in non-Abelian non-Hermitian quantum field theories

TL;DR

This paper extends Goldstone's theorem to non-Hermitian non-Abelian quantum field theories using a pseudo-Hermitian framework, analyzing symmetry breaking and Goldstone bosons in PT-symmetric regimes.

Contribution

It generalizes Goldstone's theorem to non-Hermitian non-Abelian theories with a detailed analysis of SU(2) symmetry and compares different approaches for identifying Goldstone bosons.

Findings

Goldstone theorem applies in PT-symmetric regime at exceptional points

Goldstone bosons cannot be identified at zero exceptional points

Different approaches yield different explicit forms of Goldstone boson fields

Abstract

We generalise previous studies on the extension of Goldstone's theorem from Hermitian to non-Hermitian quantum field theories with Abelian symmetries to theories possessing a glocal non-Abelian symmetry. We present a detailed analysis for a non-Hermitian field theory with two complex two component scalar fields possessing a SU(2)-symmetry and indicate how our finding extend to the general case. In the PT-symmetric regime and at the standard exceptional point the Goldstone theorem is shown to apply, although different identification procedures need to be employed. At the zero exceptional points the Goldstone boson can not be identified. Comparing our approach, based on the pseudo-Hermiticity of the model, to an alternative approach that utilises surface terms to achieve compatibility for the non-Hermitian system, we find that the explicit forms of the Goldstone boson fields are different.