On-shell consistency of the Rarita-Schwinger field formulation

TL;DR

This paper demonstrates that all bilinear couplings of a massive spin-3/2 field can be reformulated into a gauge-invariant form through explicit non-linear field redefinitions, impacting chiral effective field theories with Delta isobars.

Contribution

It provides a general proof and explicit transformation for gauge-invariant reformulation of spin-3/2 couplings, extending the understanding of field redefinitions in high-spin theories.

Findings

Any bilinear coupling can be gauge transformed.

Explicit closed-form field transformation is derived.

Implications for chiral effective field theory with Delta isobars are discussed.

Abstract

We prove that any bilinear coupling of a massive spin-3/2 field can be brought into a gauge invariant form suggested by Pascalutsa by means of a non-linear field redefinition. The corresponding field transformation is given explicitly in a closed form and the implications for chiral effective field theory with explicit Delta (1232) isobar degrees of freedom are discussed.