Methods for derivation of generalized equations in the (S, 0) ⊕ (0, S) representations of the Lorentz group1Some parts of this paper have been presented at the XI Escuela de DGFM SMF, Dec. 5-9, 2016, Playa del Carmen, QRoo, México, the IARD2018, June 4-7, 2018, Mérida, Yuc., México and the MG15 Meeting, July 1-7, Rome, Italy.

Abstract

We continue the discussion of several explicit examples of generalizations in relativistic quantum mechanics. We discussed the generalized spin-1/2 equations for neutrinos and the spin-1 equations for photon. The equations obtained by means of the Gersten-Sakurai method and those of Weinberg for spin-1 particles have been mentioned. Thus, we generalized the Maxwell and Weyl equations. Particularly, we found connections of the well-known solutions and the dark 4-spinors in the Ahluwalia-Grumiller elko model. They are also not the eigenstates of the chirality and helicity. The equations may lead to the dynamics which are different from those accepted at the present time. For instance, the photon may have non-transverse components and the neutrino may be not in the energy states and in the chirality states. The second-order equations have been considered too. They have been obtained by the Ryder method.