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 ${\varphi }_{{}_L}(p^{\mu })$ transforms as a $(0,j)$ spinor under Lorentz boosts, then ${\Theta }_{[j]}{\varphi }_{{}_L}^{\ast }(p^{\mu })$ transforms as a $(j,0)$ spinor (with a similar relationship existing between ${\varphi }_{{}_R}(p^{\mu })$ and ${\Theta }_{[j]}{\varphi }_{{}_R}^{\ast }(p^{\mu })$; where ${\Theta }_{[j]}\mathbf{J}{\Theta }_{[j]}^{-1}=-{\mathbf{J}}^{\ast }$ with ${\Theta }_{[j]}$ the well known Wigner matrix involved in the operation of time reversal) we introduce McLennan-Case type $(j,0)\oplus (0,j)$ spinors. Relative phases between ${\varphi }_{{}_R}(p^{\mu })$ and ${\Theta }_{[j]}{\varphi }_{{}_R}^{\ast }(p^{\mu })$, and ${\Theta }_{[j]}{\varphi }_{{}_L}^{\ast }(p^{\mu })$ and ${\varphi }_{{}_L}(p^{\mu })$, turn out to have physical significance and are fixed by appropriate requirements. 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 introduction of Dirac-like and Majorana-like quantum fields.

Revised and re-written version to appear in Int. J. Mod. Phys. A. At present violations of various symmetries, such as C, P, and T, are assumed to arise from interactions. It is argued that the violation is more fundamental than that and is to be found at basic level of the representations of the Lorentz group. Revtex 3.0 (20 pages)

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