Covariant representations of the de Sitter isometry group

TL;DR

This paper demonstrates that two different approaches to constructing covariant representations of the de Sitter isometry group are equivalent, leading to a unified theory of covariant fields with spin on de Sitter spacetime.

Contribution

It shows the equivalence of Nachtmann's induced representations with those from the authors' external symmetry theory, completing the framework for covariant fields on de Sitter space.

Findings

Technical details of the representations are provided for the first time.

The two methods are shown to be coherent and complementary.

A unified theory of covariant fields with spin on de Sitter spacetime is established.

Abstract

We show that the induced representations of the de Sitter isometry group proposed many years ago by Nachtmann are equivalent to those derived from our general theory of external symmetry. These methods complete each other leading to a coherent theory of covariant fields with spin on the de Sitter spacetime. Some technical details of these representations are presented here for the first time.