Relativistic vector bosons and PT-symmetry

Relativistic massive bosons with spin one are considered in several quantization schemes. In all of them the system is shown described by a non-Hermitian Hamiltonian H 6= H and helicity operator Λ. Constructively we show that in all of the contemplated schemes both these operators H and Λ prove simultaneously PT −symmetric, i.e., pseudo-Hermitian with respect to a certain not too complicated indefinite pseudo-metric operator P = P†. 1