Jean Alexandre
Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
Alexandre, Jean; Ellis, John; Millington, Peter; Seynaeve, Dries
Authors
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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Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
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https://creativecommons.org/licenses/by/4.0/
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