Symmetry properties of non-Hermitian PT-symmetric quantum field theories

Abstract

We describe recent progress in understanding the continuous symmetry properties of non-Hermitian, PT-symmetric quantum field theories. Focussing on a simple non-Hermitian theory composed of one complex scalar and one complex pseudoscalar, we revisit the derivation of Noether's theorem to show that the conserved currents of non-Hermitian theories correspond to transformations that do not leave the Lagrangian invariant. We illustrate the impact that this has on the consistent formulation of (Abelian) gauge theories by studying a non-Hermitian extension of scalar quantum electrodynamics. We consider the spontaneous breakdown of both global and local symmetries, and describe how the Goldstone theorem and the Englert-Brout-Higgs mechanism are borne out for non-Hermitian, PT-symmetric theories.

7 pages, JPCS format. Prepared for the proceedings of DISCRETE2018: the Sixth Symposium on Prospects in the Physics of Discrete Symmetries, 26 - 30 November 2018, Austrian Academy of Sciences, Vienna, to appear in the Journal of Physics: Conference Series

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• PT-symmetric quantum mechanics
• Symmetries and conservation laws in non-Hermitian field theories
• Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
• Goldstone bosons and the Englert-Brout-Higgs mechanism in non-Hermitian theories
• Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories
• Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians

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• Complex topological soliton with real energy in particle physics