Symmetries and conservation laws in non-Hermitian field theories
| Autor: | Alexandre, Jean, Millington, Peter, Seynaeve, Dries |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Phys. Rev. D 96, 065027 (2017) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevD.96.065027 |
| Popis: | 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. Comment: Discussions extended |
| Databáze: | arXiv |
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