Free field structure of the model with a spin-$\frac{3}{2}$ Rarita-Schwinger field directly coupled to a spin-$\frac{1}{2}$ field

TL;DR

This paper analyzes the free field structure of a model coupling a spin-3/2 Rarita-Schwinger field to a spin-1/2 field, focusing on the case where the gauge coupling is zero but the direct coupling remains.

Contribution

It provides a detailed analysis of the free field structure of a coupled spin-3/2 and spin-1/2 model with zero gauge coupling, extending previous work.

Findings

Detailed free field structure elucidated

Framework for perturbative expansion established

Foundation for further coupled model studies

Abstract

In earlier work we introduced an abelianized gauge field model in which a Rarita-Schwinger field is directly coupled to a spin-$\frac{1}{2}$ field, and showed that this model admits a perturbative expansion in the gauge field coupling. As a preliminary to further study of the coupled model, in this paper we present a detailed analysis of the free field structure that obtains when the dimensionless gauge coupling is set to zero, but the dimension one coupling of the spin-$\frac{3}{2}$ and spin-$\frac{1}{2}$ fields remains nonzero.