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Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories

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

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Authors

Jean Alexandre

John Ellis

Peter Millington

Dries Seynaeve



Abstract

We demonstrate the extension to parity-time (PT)-symmetric field theories of the Goldstone theorem, confirming that the spontaneous appearance of a field vacuum expectation value via minimization of the effective potential in a non-Hermitian model is accompanied by a massless scalar boson. Laying a basis for our analysis, we first show how the conventional quantization of the path-integral formulation of quantum field theory can be extended consistently to a non-Hermitian model by considering PT conjugation instead of Hermitian conjugation. The extension of the Goldstone theorem to a PT-symmetric field theory is made possible by the existence of a conserved current that does not, however, correspond to a symmetry of the non-Hermitian Lagrangian. In addition to extending the proof of the Goldstone theorem to a PT-symmetric theory, we exhibit a specific example in which we verify the existence of a massless boson at the tree and one-loop levels.

Citation

Alexandre, J., Ellis, J., Millington, P., & Seynaeve, D. (2018). Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories. Physical Review D, 98(4), Article 5001. https://doi.org/10.1103/physrevd.98.045001

Journal Article Type Article
Acceptance Date Jul 3, 2018
Online Publication Date Aug 1, 2018
Publication Date Aug 1, 2018
Deposit Date Aug 2, 2018
Publicly Available Date Mar 29, 2024
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0029
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 98
Issue 4
Article Number 5001
DOI https://doi.org/10.1103/physrevd.98.045001
Public URL https://nottingham-repository.worktribe.com/output/913382
Publisher URL https://journals.aps.org/prd/pdf/10.1103/PhysRevD.98.045001

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