| Article | |
| Report number | arXiv:2006.06656 ; KCL-PH-TH/2020-19 ; CERN-TH-2020-063 |
| Title | Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories |
| Author(s) | Alexandre, Jean (King's Coll. London) ; Ellis, John (King's Coll. London ; NICPB, Tallinn ; CERN) ; Millington, Peter (Nottingham U.) |
| Publication | 2020-12-29 |
| Imprint | 2020-06-11 |
| Number of pages | 20 |
| Note | 44 pages, revtex format; to match published version, including a revised discussion of particle mixing and oscillations |
| In: | Phys. Rev. D 102 (2020) 125030 |
| DOI | 10.1103/PhysRevD.102.125030 (publication) |
| Subject category | quant-ph ; General Theoretical Physics ; hep-th ; Particle Physics - Theory |
| Abstract | We discuss second quantization, discrete symmetry transformations and inner products in free non-Hermitian scalar quantum field theories with PT symmetry, focusing on a prototype model of two complex scalar fields with anti-Hermitian mass mixing. Whereas the definition of the inner product is unique for theories described by Hermitian Hamiltonians, its formulation is not unique for non-Hermitian Hamiltonians. Energy eigenstates are not orthogonal with respect to the conventional Dirac inner product, so we must consider additional discrete transformations to define a positive-definite norm. We clarify the relationship between canonical-conjugate operators and introduce the additional discrete symmetry C', previously introduced for quantum-mechanical systems, and show that the C'PT inner product does yield a positive-definite norm, and hence is appropriate for defining the Fock space in non-Hermitian models with PT symmetry in terms of energy eigenstates. We also discuss similarity transformations between PT-symmetric non-Hermitian scalar quantum field theories and Hermitian theories, showing that they would require modification in the presence of interactions. As an illustration of our discussion, we compare particle mixing in a Hermitian theory and in the corresponding non-Hermitian model with PT symmetry, showing how the latter maintains unitarity and exhibits mixing between scalar and pseudoscalar bosons. |
| Copyright/License | preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2020-2025 authors (License: CC-BY-4.0), sponsored by SCOAP³ |
Corresponding record in: Inspire
Record created 2020-07-01, last modified 2023-12-12
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