Rarita--Schwinger for spin 3/2 field and separation of the variables in static coordinates of de Sitter space, Schr\"{o}dinger tetrad basis

TL;DR

This paper investigates the Rarita-Schwinger formalism for a massive spin 3/2 particle in de Sitter space, achieving variable separation in static coordinates using an extended tetrad basis and Wigner D-functions.

Contribution

It introduces a covariant wave equation for spin 3/2 fields in de Sitter space and demonstrates variable separation with a reduction of radial equations.

Findings

Derived a covariant system of equations for spin 3/2 particles.

Successfully separated variables in static coordinates of de Sitter space.

Reduced the radial equations from 16 to 8 through symmetry considerations.

Abstract

Rarita-Schwinger approach to description of a massive spin 3/2 particle is investigated in static coordinates of the de Sitter space-time. The general covariant system, derived from the relevant Lagrangian, is presented as a main wave equation and additional constraints in the form of first order deferential and algebraic relations. With the use of an extended Schr\"{o}dinger tetrad basis and technique of Wigner D-functions the separation of the variable performed. 16 radial equations reduce to 8 ones through diagonalization of $P$-inversion operator for spin 3/2 field.