Fermions via spinor-valued one-forms

TL;DR

This paper introduces a novel Lagrangian formulation using spinor-valued one-forms that describes a propagating spin 1/2 particle, contrasting the traditional use for spin 3/2 particles in supergravity.

Contribution

It presents a new approach to describe spin 1/2 particles with spinor-valued one-forms, expanding the applications of Rarita-Schwinger fields beyond supergravity.

Findings

A Lagrangian for spin 1/2 particles using spinor-valued one-forms

Demonstration that such fields can propagate spin 1/2 particles

Contrasts with the traditional use for spin 3/2 particles

Abstract

Spinor-valued one-forms (Rarita-Schwinger fields) are normally used in the context of supergravity, where they describe spin 3/2 particles (gravitinos). Indeed, when decomposed into irreducible representations of the Lorentz group such a field contains both a spin 1/2 and a spin 3/2 component, and the Rarita-Schwinger Lagrangian is designed to make only the spin 3/2 propagate. We point out that the opposite construction is also possible, and give a spinor-valued one-form field Lagrangian that describes a propagating spin 1/2 particle.