Ivan I. Yuryk (Ukrainian State University of Food Technologies, Kyiv)

Unitary irreducible representations of group ${\rm P}(1,n)$ in ${\rm SO}(1,n)$- and ${\rm P}(1,n-k)$-basises

Abstract:
The reduction problem of unitary irreducible representations of Poincaré group ${\rm P}(1,n)$ with respect to the representations of its subgroups ${\rm SO}(1,n)$ and ${\rm P}(1,n-k)$ is considered. The actions of the generators in ${\rm P}(1,n-k)$-basis are explicitly defined. On the grounds of the generalization of WignerૻEckart theorem for noncompact groups the matrix elements of the operators in ${\rm SO}(1,n)$-basis are obtained.