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Symmetries and conservation laws in non-Hermitian field theories

Alexandre, Jean; Millington, Peter; Seynaeve, Dries

Symmetries and conservation laws in non-Hermitian field theories Thumbnail


Jean Alexandre

Peter Millington

Dries Seynaeve


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
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 2470-0010
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 96
Issue 6
Public URL
Publisher URL


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