Wave equations for spin 3/2 quantum fields

TL;DR

This paper reviews various formulations of wave equations for spin-3/2 quantum fields, analyzing their structures and exploring new algebraic frameworks, including a novel representation, to advance understanding of high-spin particle descriptions.

Contribution

It compares existing spin-3/2 wave equations, explores the DKP formalism for such fields, and introduces a new representation combining multiple Lorentz group components.

Findings

Recovery of the Rarita-Schwinger representation

Identification of a new combined Lorentz representation for spin 3/2

Analysis of covariant operators in different formalisms

Abstract

In this work, we review formulations of wave equations for spin-3/2 fields constructed from different Lorentz group representations. We analyze the Joss-Weinberg single-spin chiral representation and the double-spin chiral representation, focusing on the structure of their covariant operators. We explore the Duffin-Kemmer-Petiau (DKP) formalism and its algebraic properties, originally introduced for spin--0 and spin-1 particles, and here considered as a potential framework for spin 3/2. As a result, we recover the well-known Rarita-Schwinger representation and we find a new possibility in the $(3/2,0) \oplus (0,3/2) \oplus (1,1/2) \oplus (1/2,1)$ representation.