Quantum electrodynamics of spin 3/2

TL;DR

This paper develops a consistent quantum electrodynamics framework for spin 3/2 particles that includes the transverse spin 1/2 component, proposing a new extension to the Standard Model with potential experimental implications.

Contribution

It introduces a generalized mass term for spin 3/2 particles, ensuring causality and consistency while allowing the spin 1/2 component to propagate, and suggests a new Standard Model extension involving muons and heavy partners.

Findings

Interaction is consistent without superluminal propagation.

Constructed a causal, quantized field with proper projection operators.

Derived bounds on new particle masses from electroweak data.

Abstract

Electromagnetic interactions of the spin 3/2 particle are investigated while allowing the propagation of the transverse spin 1/2 component present in the reducible Rarita-Schwinger vector-spinor. This is done by allowing a more general form for the mass term, while leaving the kinetic terms untouched. We find that the interaction is consistent and does not lead to superluminal propagation for a range of the mass parameter where the spin 1/2 component is lighter than the spin 3/2 component, in contrast to the traditional value whereby the spin 1/2 component is removed by making it infinitely massive. The hyperbolicity condition is found to be independent of the magnitude of the electromagnetic field, and the canonically quantized field is constructed to be causal. We then provide appropriate projection operators which reproduce the spin-sum expressions and enable the construction of a physically acceptable propagator. Finally, we suggest a scheme for extension of the Standard Model with Rarita-Schwinger multiplets and identify the muon as the spin 1/2 component of the new multiplet which in addition contains a new, heavy partner of the muon of spin 3/2. The scattering cross-section e+, e- \to {\mu}+, {\mu}- is calculated within this theory, compared to QED, and finally a bound on the new particle's mass is obtained from precision electroweak measurements.