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

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.

arXiv comment29 pages, revtex format; to match published version

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• Poincaré symmetries and representations in pseudo-Hermitian quantum field theory
• Wilsonian approach to the interaction ${\varphi }^2(i\varphi {)}^{\epsilon }$
• Oscillators with imaginary coupling: spectral functions in quantum mechanics and quantum field theory
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system