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

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.

14 pages, 2 figures

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Cited by in corpus (6)

• 't Hooft-Polyakov monopoles in non-Hermitian quantum field theory
• On the consistency of a non-Hermitian Yukawa interaction
• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Renormalisation group flows connecting a $4-\epsilon$ dimensional Hermitian field theory to a $\mathcal{P}\mathcal{T}$-symmetric theory for a fermion coupled to an axion
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system