The C Operator in PT-Symmetric Quantum Field Theory Transforms as a   Lorentz Scalar
  A non-Hermitian Hamiltonian has a real positive spectrum and exhibits unitary time evolution if the Hamiltonian possesses an unbroken PT (space-time reflection) symmetry. The proof of unitarity requires the construction of a linear operator called C. It is shown here that C is the complex extension of the intrinsic parity operator and that the C operator transforms under the Lorentz group as a scalar. 
Carl M. Bender, Sebastian F. Brandt, Jun-Hua Chen, and Qinghai Wang