CLEBSCH-GORDAN AND RACAH COEFFICIENTS OF THE POINCARE GROUP

Clebsch-Gordan and Racah coefficients of the Poincaré group are needed in many applications, including relativistic quantum mechanics. Due to the structure of the Poincaré group, it is possible to couple states of arbitrary spin and (positive) mass together simultaneously, rather than in a stepwise fashion as is conventionally done to get the Clebsch-Gordan coefficients of many-particle states. It is shown that such simultaneously coupled states depend on relativistically invariant variables and can be symmetrized in a relatively straightforward fashion. Coefficients are computed which connect simultaneously coupled states to stepwise-coupled states. These coefficients are then used to obtain Racah coefficients connecting different stepwise-coupled states. © 1992.