  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.
