On the "old" and "new" relativistic wave equations for the particle having spin s=3/2

TL;DR

This paper introduces a new relativistic wave equation for spin 3/2 particles with only 8 components, comparing it to known equations and establishing its consistency at quantum mechanics and field theory levels.

Contribution

It proposes a novel wave equation for spin 3/2 particles with fewer components and connects quantum mechanics and field theory through an extended Foldy--Wouthuysen transformation.

Findings

Wave function has only 8 components for particle-antiparticle doublet.

Comparison shows the new equation differs from known equations.

Transformation links quantum mechanics and field theory levels.

Abstract

Relativistic wave equation of motion without redundant components for the particle having spin 3/2 has been considered. In order to show the newness a comparison with the known equations for the spin s=3/2 field is given. Therefore, the brief review of the relativistic wave equations for the particle with spin s=3/2 is given. In our equation the wave function for the particle-antiparticle doublet has only 8 components. The consideration is carried out both at the level of relativistic quantum mechanics and at the level of local field theory. The extended Foldy--Wouthuysen transformation, which gives the operator link between these two levels is suggested.