Covariant fields on anti-de Sitter spacetimes

TL;DR

This paper analyzes covariant free fields of any spin on anti-de Sitter spacetimes, revealing their transformation properties, representation equivalences, and the non-existence of a universal mass condition unlike in special relativity.

Contribution

It demonstrates that covariant fields on anti-de Sitter spacetime transform under specific isometry group representations and establishes their equivalence with certain unitary irreducible representations, highlighting differences from flat spacetime.

Findings

Covariant fields transform under isometry group representations.

Covariant representations with unique spin are equivalent to discrete unitary irreducible representations.

A universal mass condition cannot be formulated on anti-de Sitter spacetime.

Abstract

The covariant free fields of any spin on anti-de Sitter spacetimes are studied, pointing out that these transform under isometries according to covariant representations of the anti-de Sitter isometry group, induced by those of the Lorentz group. Applying the method of ladder operators it is shown that the covariant representations with unique spin are equivalent with discrete unitary irreducible representations of positive energy of the universal covering group of the isometry one. The action of the Casimir operators is studied finding how the weights of these representations may depend on the mass and spin of the covariant field. The conclusion is that on anti-de Sitter spacetime one cannot formulate an universal mass condition as in special relativity.