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arXiv · 1808.00944

Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories

Jean Alexandre·John Ellis·Peter Millington·Dries Seynaeve
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Abstract

We discuss $\mathcal{PT}$-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 generalise the Englert-Brout-Higgs mechanism to $\mathcal{PT}$-symmetric field theories, opening the way to constructing non-Hermitian extensions of the Standard Model and new scenarios for particle model-building.

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Jean Alexandre, John Ellis, Peter Millington, Dries Seynaeve. 2018-08-02. Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories. https://doi.org/10.1103/physrevd.99.075024

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