Symmetries and conservation laws in non-Hermitian field theories

Alexandre, Jean; Millington, Peter; Seynaeve, Dries

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.

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

• Journal Article Type: Article
• Acceptance Date: Sep 12, 2017
• Online Publication Date: Sep 29, 2017
• Publication Date: Sep 29, 2017
• Deposit Date: Nov 2, 2017
• Publicly Available Date: Nov 2, 2017
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 96
• Issue: 6
• DOI: https://doi.org/10.1103/PhysRevD.96.065027
• Public URL: https://nottingham-repository.worktribe.com/output/882579
• Publisher URL: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.065027
• Contract Date: Nov 2, 2017