  We study the theory of the Lorentz group (1/2,0)+(0,1/2) representation in
the helicity basis of the corresponding 4-spinors. As Berestetski, Lifshitz and
Pitaevskii mentioned, the helicity eigenstates are not the parity eigenstates.
Relations with the Gelfand-Tsetlin-Sokolik-type quantum field theory are
discussed. Finally, a new form of the parity operator (which commutes with the
Hamiltonian) is proposed in the Fock space.
