## 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 [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.

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.

Original language | English |
---|---|

Journal | Phys. Rev. D |

DOIs | |

Publication status | Published - 15 Sept 2022 |