Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory

• URL: http://arxiv.org/abs/2201.11061v2
• Date: Fri, 9 Sep 2022 12:54:36 GMT
• Title: Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory
• Authors: Jean Alexandre, John Ellis, Peter Millington
• Abstract summary: We consider a prototype model containing a single Dirac fermion with a parity-odd, anti-Hermitian mass term. In the phase of unbroken PT symmetry, this Dirac fermion model is equivalent to a Hermitian theory under a similarity transformation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We extend to a non-Hermitian fermionic quantum field theory with PT symmetry our previous discussion of second quantization, discrete symmetry transformations, and inner products in a scalar field theory [arXiv:2006.06656]. For illustration, we consider a prototype model containing a single Dirac fermion with a parity-odd, anti-Hermitian mass term. In the phase of unbroken PT symmetry, this Dirac fermion model is equivalent to a Hermitian theory under a similarity transformation, with the non-Hermitian nature of the model residing only in the spinor structure, whereas the algebra of the creation and annihilation operators is just that of a Hermitian theory.

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