Bala Ali Rajabov | Searcharxiv

arXiv2018

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

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 Poincaré 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.

physics.gen-ph↗

arXiv2017

The theory of representations of groups $SO_{0}(2,1)$ and $ISO(2,1)$. Wigner coefficients of the group $SO_{0}(2,1)$

This paper is devoted to the representations of the groups $SO (2,1)$ and $ISO (2,1)$. Those groups have an important role in cosmology, elementary particle theory and mathematical physics. Irreducible unitary representations of the principal continuous and supplementary as well as discrete series were obtained. Explicit expressions for spherical functions of the group $SO_0(2,1)$ are obtained through the Gauss hypergeometric functions. The Wigner coefficients of the group $SO_{0}(2,1)$ were computed and their explicit expressions using the bilateral series were represented. The results could be used to study the non-degenerate representations of the de Sitter group $SO(3,2)$.

math-ph↗