Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories

Alexandre, Jean; Ellis, John; Millington, Peter

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.

Citation

Alexandre, J., Ellis, J., & Millington, P. (2020). Discrete spacetime symmetries and particle mixing in non-Hermitian scalar quantum field theories. Physical Review D, 102(12), https://doi.org/10.1103/PhysRevD.102.125030

• Journal Article Type: Article
• Acceptance Date: Nov 21, 2020
• Online Publication Date: Dec 28, 2020
• Publication Date: Dec 28, 2020
• Deposit Date: Jan 2, 2021
• Publicly Available Date: Jan 6, 2021
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 102
• Issue: 12
• DOI: https://doi.org/10.1103/PhysRevD.102.125030
• Keywords: Physics and Astronomy (miscellaneous)
• Public URL: https://nottingham-repository.worktribe.com/output/5184234
• Publisher URL: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.102.125030