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

Alexandre, Jean; Ellis, John; Millington, Peter; Seynaeve, Dries


Jean Alexandre

John Ellis

Peter Millington

Dries Seynaeve


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, J., Ellis, J., Millington, P., & Seynaeve, D. (2019). Gauge invariance and the Englert-Brout-Higgs mechanism in non-Hermitian field theories. Physical Review D, 99(7), 1-9.

Journal Article Type Article
Acceptance Date Mar 18, 2019
Online Publication Date Apr 19, 2019
Publication Date Apr 19, 2019
Deposit Date Apr 22, 2019
Publicly Available Date Apr 29, 2019
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0029
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 99
Issue 7
Article Number 075024
Pages 1-9
Public URL
Publisher URL


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