Symmetries and conservation laws in non-Hermitian field theories
Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for PT-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the PT-conjugate variables, allowing for an unambiguous definition of the equ...
| Main Authors: | , , |
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| Format: | Article |
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American Physical Society
2017
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| Online Access: | https://eprints.nottingham.ac.uk/47778/ |
| _version_ | 1848797627160723456 |
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| author | Alexandre, Jean Millington, Peter Seynaeve, Dries |
| author_facet | Alexandre, Jean Millington, Peter Seynaeve, Dries |
| author_sort | Alexandre, Jean |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for PT-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the PT-conjugate variables, allowing for an unambiguous definition of the equations of motion. After discussing the resulting constraints on the consistency of the variational procedure, we show that the invariance of a non-Hermitian Lagrangian under a continuous symmetry transformation does not imply the existence of a corresponding conserved current. Conserved currents exist, but these are associated with transformations under which the Lagrangian is not invariant and which reflect the well-known interpretation of PT-symmetric theories in terms of systems with gain and loss. A formal understanding of this unusual feature of non-Hermitian theories requires a careful treatment of Noether’s theorem, and we give specific examples for illustration. |
| first_indexed | 2025-11-14T20:06:53Z |
| format | Article |
| id | nottingham-47778 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:06:53Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-477782020-05-04T19:06:30Z https://eprints.nottingham.ac.uk/47778/ Symmetries and conservation laws in non-Hermitian field theories Alexandre, Jean Millington, Peter Seynaeve, Dries Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for PT-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the PT-conjugate variables, allowing for an unambiguous definition of the equations of motion. After discussing the resulting constraints on the consistency of the variational procedure, we show that the invariance of a non-Hermitian Lagrangian under a continuous symmetry transformation does not imply the existence of a corresponding conserved current. Conserved currents exist, but these are associated with transformations under which the Lagrangian is not invariant and which reflect the well-known interpretation of PT-symmetric theories in terms of systems with gain and loss. A formal understanding of this unusual feature of non-Hermitian theories requires a careful treatment of Noether’s theorem, and we give specific examples for illustration. American Physical Society 2017-09-15 Article PeerReviewed Alexandre, Jean, Millington, Peter and Seynaeve, Dries (2017) Symmetries and conservation laws in non-Hermitian field theories. Physical Review D, 96 (6). 065027. ISSN 2470-0010 https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.065027 doi:10.1103/PhysRevD.96.065027 doi:10.1103/PhysRevD.96.065027 |
| spellingShingle | Alexandre, Jean Millington, Peter Seynaeve, Dries Symmetries and conservation laws in non-Hermitian field theories |
| title | Symmetries and conservation laws in non-Hermitian field theories |
| title_full | Symmetries and conservation laws in non-Hermitian field theories |
| title_fullStr | Symmetries and conservation laws in non-Hermitian field theories |
| title_full_unstemmed | Symmetries and conservation laws in non-Hermitian field theories |
| title_short | Symmetries and conservation laws in non-Hermitian field theories |
| title_sort | symmetries and conservation laws in non-hermitian field theories |
| url | https://eprints.nottingham.ac.uk/47778/ https://eprints.nottingham.ac.uk/47778/ https://eprints.nottingham.ac.uk/47778/ |