Poincar\'{e} symmetries and representations in pseudo-Hermitian quantum field theory
This paper explores quantum field theories with pseudo-Hermitian Hamiltonians, where PT-symmetric Hamiltonians serve as a special case. In specific regimes, these pseudo-Hermitian Hamiltonians have real eigenspectra, orthogonal eigenstates, and unitary time evolution. So far, most pseudo-Hermitian q...
Gespeichert in:
Veröffentlicht in: | arXiv.org 2024-04 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | This paper explores quantum field theories with pseudo-Hermitian Hamiltonians, where PT-symmetric Hamiltonians serve as a special case. In specific regimes, these pseudo-Hermitian Hamiltonians have real eigenspectra, orthogonal eigenstates, and unitary time evolution. So far, most pseudo-Hermitian quantum field theories have been constructed using analytic continuation or by adding non-Hermitian terms to otherwise Hermitian Hamiltonians. However, in this paper, we take a different approach. We construct pseudo-Hermitian scalar and fermionic quantum field theories from first principles by extending the Poincaré algebra to include non-Hermitian generators. This allows us to develop consistent pseudo-Hermitian quantum field theories, with Lagrangian densities that transform appropriately under the proper Poincaré group. By doing so, we establish a more solid theoretical foundation for the emerging field of non-Hermitian quantum field theory. |
---|---|
ISSN: | 2331-8422 |
DOI: | 10.48550/arxiv.2307.16805 |