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We discuss PT-symmetric Abelian gauge field theories as well as their extension to the Englert-Brout-Higgs mechanism for generating a mass for a vector boson. Gauge invariance is not straightforward, and we discuss the different related problems as well as a solution which consists in coupling the gauge field to a current that is not conserved. Non-Hermiticity then necessarily precludes the Lorenz gauge condition but nevertheless allows for a consistent formulation of the theory. We therefore generalize the Englert-Brout-Higgs mechanism to PT-symmetric field theories, opening the way to constructing non-Hermitian extensions of the Standard Model and new scenarios for particle model building.
Alexandre et al. (Fri,) studied this question.
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