On the existence of additional solutions for equations in the $(1/2,0)\oplus (0,1/2)$ representation space

TL;DR

This paper investigates the solutions of certain neutrino equations in the (1/2,0)⊕(0,1/2) representation space, revealing the existence of additional, potentially acausal solutions similar to those in Dirac-like equations.

Contribution

It derives and analyzes dispersion relations for neutrino equations proposed by Ahluwalia, identifying additional solutions and their properties within the spinor framework.

Findings

Equations contain acausal solutions similar to Dirac-like second-order equations.

Additional solutions are shown to exist without imposing certain constraints.

Analysis based on Wigner rules and Ryder-Burgard relation.

Abstract

We analyze dispersion relations of the equations recently proposed by Ahluwalia for describing neutrino. Equations for type-II spinors are deduced on the basis of the Wigner rules for left- and right- 2-spinors and the Ryder-Burgard relation. It is shown that equations contain acausal solutions which are similar to those of the Dirac-like second-order equation. The latter is obtained in a similar way, provided that we do not apply to any constraints in the process of its deriving.