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

Fring, A. ORCID: 0000-0002-7896-7161 and Taira, T. (2020). Pseudo-Hermitian approach to Goldstone’s theorem in non-Abelian non-Hermitian quantum field theories. Physical Review D, 101(4), 045014.. doi: 10.1103/physrevd.101.045014

Abstract

We generalize 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 an SU(2) symmetry and indicate how our findings extend to the general case. In the PT-symmetric regime (parity and time-reversal) 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 utilizes surface terms to achieve compatibility for the non-Hermitian system, we find that the explicit forms of the Goldstone boson fields are different.

Publication Type: Article
Additional Information: Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Subjects: Q Science > QA Mathematics
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
Date Deposited: 27 Feb 2020 16:01
URI: https://openaccess.city.ac.uk/id/eprint/23806
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