Weyl and Majorana for Neutral Particles

TL;DR

This paper critically compares different formalisms for neutral particles, revealing contradictions and incompatibilities, and suggests that helicity basis calculations are more consistent for spin-1/2 and spin-1 particles.

Contribution

It demonstrates the incompatibility of Majorana and Dirac formalisms for neutral particles across various spins and bases, clarifying the physical and mathematical consistency issues.

Findings

Incompatibility of Majorana and Dirac formalisms for neutral particles.

Helicity basis provides more consistent results.

Contradictions found in various formalisms for neutral particles.

Abstract

We compare various formalisms for neutral particles. It is found that they contain unexplained contradictions. Next, we investigate the spin-1/2 and spin-1 cases in different bases. Next, we look for relations with the Majorana-like field operator. We show explicitly incompatibility of the Majorana anzatzen with the Dirac-like field operators in both the original Majorana theory and its generalizations. Several explicit examples are presented for higher spins too. It seems that the calculations in the helicity basis only give mathematically and physically reasonable results.