The physical meaning of the de Sitter invariants

TL;DR

This paper analyzes the Lie algebra invariants of matter fields in de Sitter spacetime, expressing Casimir eigenvalues in terms of physical parameters and connecting them to Poincare invariants in the flat limit.

Contribution

It provides closed-form expressions for Casimir operators of de Sitter covariant representations and relates them to physical quantities like mass and spin.

Findings

Casimir eigenvalues depend on rest energy and spin

Eigenvalues expressed in terms of mass and spin for various fields

In the flat limit, invariants reduce to Poincare group invariants

Abstract

We study the Lie algebras of the covariant representations transforming the matter fields under the de Sitter isometries. We point out that the Casimir operators of these representations can be written in closed forms and we deduce how their eigenvalues depend on the field's rest energy and spin. For the scalar, vector and Dirac fields, which have well-defined field equations, we express these eigenvalues in terms of mass and spin obtaining thus the principal invariants of the theory of free fields on the de Sitter spacetime. We show that in the flat limit we recover the corresponding invariants of the Wigner irreducible representations of the Poincare group.