  We study the theory of the (1/2,0)+(0,1/2) representation in helicity basis.
Helicity eigenstates are not the parity eigenstates. This is in accordance with
the consideration of Berestetskii, Lifshitz and Pitaevskii. Relations to the
Gelfand-Tsetlin-Sokolik-type quantum field theory are discussed. Finally, a new
form of the parity operator is proposed. It commutes with the Hamiltonian.
