CLEBSCH-GORDAN COEFFICIENTS OF THE LORENTZ GROUP

Gel land and Graev's results [1] are used to show that the homogeneous components of the one-particle helical state with zero mass vertical bar k lambda; rho > (k(2) = 0) form the space of the irreducible representation chi(i rho + lambda, i rho - lambda) of the Lorentz group. In a spherical coordinate system it is identical with the space of functions f(u) on the group U of unitary matrices. A decomposition of the space of the direct product of these representations into invariant subspaces is obtained as well as an integral representation for the Clebsch-Gordan coefficients in a canonical basis.