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

TY - JOUR

T1 - Discrete spacetime symmetries, second quantization, and inner products in a non-Hermitian Dirac fermionic field theory

AU - Alexandre, Jean

AU - Ellis, John

AU - Millington, Peter

PY - 2022/9/15

Y1 - 2022/9/15

N2 - 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 [Phys. Rev. D 102, 125030 (2020)]. 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.

AB - 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 [Phys. Rev. D 102, 125030 (2020)]. 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.

UR - https://arxiv.org/pdf/2201.11061.pdf

U2 - 10.1103/PhysRevD.106.065003

DO - 10.1103/PhysRevD.106.065003

M3 - Article

JO - Phys. Rev. D

JF - Phys. Rev. D

ER -