On the Clebsch-Gordan expansion for the Lorentz group in n dimensions

Abstract

We study the tensor product decomposition of two unitary class I (“scalar”) representations of the generalized Lorentz group. Conditions are found under which only principal series representations contribute to the decomposition. Normalized Clebsch-Gordan kernels are evaluated which satisfy a completeness and orthogonality relation. Identifies are found for the analytically continued Clebsch-Gordan kernels at partially equivalent integer points. The results are applied elsewhere [9, 4] to the nonperturbative analysis of conformal invariant quantum field theory.