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Symmetries and conservation laws in non-Hermitian field theories

Alexandre, Jean; Millington, Peter; Seynaeve, Dries

Authors

Jean Alexandre

Dries Seynaeve



Abstract

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.

Journal Article Type Article
Publication Date Sep 29, 2017
Journal Physical Review D
Print ISSN 2470-0010
Electronic ISSN 2470-0010
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 96
Issue 6
APA6 Citation Alexandre, J., Millington, P., & Seynaeve, D. (2017). Symmetries and conservation laws in non-Hermitian field theories. Physical Review D, 96(6), https://doi.org/10.1103/PhysRevD.96.065027
DOI https://doi.org/10.1103/PhysRevD.96.065027
Publisher URL https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.065027
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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