Methods for Derivation of Generalized Equations in the (S,0)+(0,S) Representations of the Lorentz Group

TL;DR

This paper explores generalized equations in relativistic quantum mechanics for particles like neutrinos and photons, revealing potential new dynamics and connections to dark spinor models, extending classical formulations.

Contribution

It introduces new generalized equations for spin-1/2 and spin-1 particles using various methods, linking them to dark spinor models and suggesting alternative particle dynamics.

Findings

Neutrinos and photons may exhibit non-standard energy and chirality states.

Connections established between generalized equations and dark 4-spinors.

Potential for non-transverse photon components and unconventional neutrino behavior.

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 {\it 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.