THEORY OF NEUTRAL PARTICLES: MCLENNAN-CASE CONSTRUCT FOR NEUTRINO, ITS GENERALIZATION, AND A NEW WAVE EQUATION

Abstract

Continuing our recent argument where we constructed a FNBWW type spin-1 boson having opposite relative intrinsic parity to that of the associated antiparticle, we now study eigenstates of the charge conjugation operator. Based on the observation that if ϕ_L(p^μ) transforms as a (0, j) spinor under Lorentz boosts, then transforms as a (j, 0) spinor [with a similar relationship existing between ϕ_R(p^μ) and where w ith Θ[j] the well-known Wigner matrix involved in the operation of time reversal] we introduce McLennan-Case type (j, 0)⊗(0, j) spinors. Relative phases between ϕ_R(p^μ) and and and ϕ_L(p^μ), turn out to have physical significance and are fixed by appropriate requirements. An explicit construction, and a series of physically relevant properties, for these spinors are obtained for spin-1/2 and spin-1 culminating in the construction of a new wave equation and the introduction of Dirac-like and Majorana-like quantum fields.