Dvoeglazov V. V. Different Quantum Field Constructions in the (1/2,0)+(0,1/2) Representation (443K, PDF, zipped, uuencoded) ABSTRACT. We present another concrete realization of a quantum field theory, envisaged many years ago by Bargmann, Wightman and Wigner. Considering the special case of the (1/2,0)+(0,1/2) field and developing the Majorana-McLennan-Case-Ahluwalia construction for neutrino we show that fermion and its antifermion can have the same intrinsic parity. The construction can be applied to explain the present situation in neutrino physics.