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

被引:25
作者
Alexandre, Jean [1 ]
Ellis, John [1 ,2 ,3 ]
Millington, Peter [4 ]
机构
[1] Kings Coll London, Dept Phys, London WC2R 2LS, England
[2] NICPB, Ravala 10, EE-10143 Tallinn, Estonia
[3] CERN, Theoret Phys Dept, CH-1211 Geneva 23, Switzerland
[4] Univ Nottingham, Sch Phys & Astron, Nottingham NG7 2RD, England
基金
英国科学技术设施理事会;
关键词
D O I
10.1103/PhysRevD.102.125030
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
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.
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页数:20
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