The physical meaning of the de Sitter invariants

Details The physical meaning of the de Sitter invariants The physical meaning of the de Sitter invariants

2010-06-08

arxiv.org/abs/1006.1472v6

Gen.Rel.Grav.43:1639-1656,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages no figures

Scientific paper

10.1007/s10714-011-1145-2

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.

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