Non-minimal coupling for spin 3/2 fields

TL;DR

This paper explores the electromagnetic coupling of spin 3/2 fields, emphasizing the necessity of non-minimal coupling involving the electromagnetic field strength, aligning with supersymmetry requirements and gyromagnetic ratio constraints.

Contribution

It demonstrates that minimal coupling is insufficient for spin 3/2 fields and proposes a non-minimal coupling approach consistent with supergravity and supersymmetric particle theories.

Findings

Non-minimal coupling involves electromagnetic field strength.

Coupling aligns with gyromagnetic ratio g=2.

Extension to non-Abelian Yang-Mills fields discussed.

Abstract

The problem of the electromagnetic coupling for spin 3/2 fields is discussed. Following supergravity and some recent works in the field of classical supersymmetric particles, we find that the electromagnetic coupling must not obey a minimal coupling in the sense that one needs to consider not only the electromagnetic potential but also the coupling of the electromagnetic field strenght. This coupling coincides with the one found by Ferrara {\it et al} by requiring that the gyromagnetic ratio be 2. Coupling with non-Abelian Yang-Mills fields is also discussed.