Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories
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...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2018
|
| Online Access: | https://eprints.nottingham.ac.uk/53415/ |
| _version_ | 1848798936272207872 |
|---|---|
| author | Alexandre, Jean Ellis, John Millington, Peter Seynaeve, Dries |
| author_facet | Alexandre, Jean Ellis, John Millington, Peter Seynaeve, Dries |
| author_sort | Alexandre, Jean |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:27:41Z |
| format | Article |
| id | nottingham-53415 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T20:27:41Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-534152018-08-22T15:27:50Z https://eprints.nottingham.ac.uk/53415/ Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories Alexandre, Jean Ellis, John Millington, Peter Seynaeve, Dries 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. American Physical Society 2018-08-01 Article PeerReviewed application/pdf en cc_by https://eprints.nottingham.ac.uk/53415/1/PhysRevD.98.045001.pdf Alexandre, Jean, Ellis, John, Millington, Peter and Seynaeve, Dries (2018) Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories. Physical Review D, 98 (4). p. 5001. ISSN 2470-0010 https://journals.aps.org/prd/pdf/10.1103/PhysRevD.98.045001 10.1103/physrevd.98.045001 10.1103/physrevd.98.045001 10.1103/physrevd.98.045001 |
| spellingShingle | Alexandre, Jean Ellis, John Millington, Peter Seynaeve, Dries Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories |
| title | Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories |
| title_full | Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories |
| title_fullStr | Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories |
| title_full_unstemmed | Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories |
| title_short | Spontaneous symmetry breaking and the Goldstone theorem in non-Hermitian field theories |
| title_sort | spontaneous symmetry breaking and the goldstone theorem in non-hermitian field theories |
| url | https://eprints.nottingham.ac.uk/53415/ https://eprints.nottingham.ac.uk/53415/ https://eprints.nottingham.ac.uk/53415/ |