Majorana-Like (j,0)+(0,j) Representation Spaces: Construction and Physical Interpretation

TL;DR

This paper extends the Majorana formalism to arbitrary spin (j,0)+(0,j) spaces, constructing a wave equation for spin-1 and exploring its unique classical and quantum properties with implications for parity violation and grand unified theories.

Contribution

It introduces a generalized Majorana-like formalism for arbitrary spin spaces and develops a corresponding wave equation for spin-1, revealing novel structural features.

Findings

Constructed a wave equation for spin-1 (j,0)+(0,j) spinors.

Discovered unusual classical and quantum field structures.

Discussed relevance to parity violation and grand unified theories.

Abstract

We present a formalism that extends the Majorana-construction to arbitrary spin (j,0)+(0,j) representation spaces. For the example case of spin-1, a wave equation satisfied by the Majorana-like (1,0)+(0,1) spinors is constructed and its physical content explored. The (j,0)+(0,j) Majorana-construct is found to possess an unusual classical and quantum field theoretic structure. Relevance of our formalism to parity violation, hadronic phenomenologies, and grand unified field theories is briefly pointed out.