The contraction of the representations of the group $SO(4,1)$ and cosmological interpretation

Abstract

We consider the operation of contraction of unitary irreducible representations of the de Sitter group $ SO(4,1) $. It is shown that a direct sum of unitary irreducible representations of the Poincar\'{e} group with different signs of the rest mass is obtained as a result of contraction. The results obtained are used to interpret the phenomena of "dark matter" and "dark energy" in terms of the elementary quantum systems of de Sitter's world.