Theory of neutral particles: McLennan-Case construct for neutrino, its generalization, and a new wave equation

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 phi(L)(p(mu)) transforms as a (0, j) spinor under Lorentz boosts, then -([j])phi((L))*(p(mu)) transforms as a (j, 0) spinor [with a similar relationship existing between phi(R)(p(mu)) and -([j])phi(R)*(p(mu)); where -([j])J-(-1)([j]) = -J* with -([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 phi(R)(p(mu)) and -([j])phi(R)*(p(mu)), and phi(L)(p(mu)), 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.