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.

29 pages, revtex format; to match published version

References in corpus (8)

• Flavour Covariant Transport Equations: an Application to Resonant Leptogenesis
• Symmetries and conservation laws in non-Hermitian field theories
• Spontaneously Breaking Non-Abelian Gauge Symmetry in Non-Hermitian Field Theories
• Pseudo-Hermitian approach to Goldstone's theorem in non-Abelian non-Hermitian quantum field theories
• Foldy-Wouthuysen transformation for non-Hermitian Hamiltonians
• From Generalized Dirac Equations to a Candidate for Dark Energy
• Relativistic PT-symmetric fermionic theories in 1+1 and 3+1 dimensions
• On the consistency of a non-Hermitian Yukawa interaction

Cited by in corpus (5)

• 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