Question

For fermion, is charge conjugate operator $C$ an anti-unitary operator?

Answer 1

For fermion, is charge conjugate operator an anti-unitary operator? In condensed matter theory, is called "particle-hole inversion", such that C 2 = − 1 , for fermionic state. In high energy physics, just like most of the QFT textbooks, is introduced from Dirac field, satisfies C 2 = 1 , even for fermionic state

Answer 2

 a reason for the difference is that in QFT one wants to have CC representing also an observables and CC is therefore defined in order to satisfy C∗=CC∗=C and thus the unitarity condition reads CC=ICC=I.