Bispinor Formulation of Spin 3/2 Field Theory

TL;DR

This paper proposes a novel bispinor formulation for the spin 3/2 field equation, extending relativistic equations based on spin operators and Hamiltonians, but encounters limitations in reducing to the Klein-Gordon form.

Contribution

It introduces a new bispinor approach for spin 3/2 fields, generalizing relativistic equations similar to Dirac and Maxwell, and explores its theoretical properties.

Findings

New bispinor formulation for spin 3/2 fields

Generalization of relativistic equations based on spin operators

Inability to reduce to Klein-Gordon form for all wave functions

Abstract

In this paper, we investigate an alternative formulation for spin 3/2 field equation. First we will review equation of motion of Dirac and Maxwell, and then construct the equation for spin 3/2 in the similar fashion. Our method actually a generalization of relativistic equation of motion based on spin operator and Hamiltonian similar to Dirac and Maxwell equation in ref. [1] pp. 50. Furthermore, we could not bring the equation to the Klein Gordon limit for every wave function component in spin 3/2 formalism.