Causal Propagation of a Charged Spin 3/2 Field in an External Electromagnetic Background

TL;DR

This paper develops a Lagrangian for a charged spin 3/2 field in a constant electromagnetic background that avoids known causality and hyperbolicity issues through specific non-minimal couplings, ensuring only physical degrees of freedom propagate.

Contribution

It introduces a novel Lagrangian formulation for a massive charged spin 3/2 field that maintains causality and hyperbolicity without extra fields or equations.

Findings

Successfully propagates only physical degrees of freedom

Avoids Velo-Zwanziger acausality

Ensures hyperbolic equations of motion

Abstract

We present a Lagrangian for a massive, charged spin 3/2 field in a constant external electromagnetic background, which correctly propagates only physical degrees of freedom inside the light cone. The Velo-Zwanziger acausality and other pathologies such as loss of hyperbolicity or the appearance of unphysical degrees of freedom are avoided by a judicious choice of non-minimal couplings. No additional fields or equations besides the spin 3/2 ones are needed to solve the problem.