Orientations of point groups-phase choices in the Racah-Wigner algebra

Abstract

The SO3-SO2-3jm's (the '3j symbols' of angular momentum) are known to incorporate no information about the orientation of axes and may be calculated from a knowledge of character theory alone, together with some freedom of choice of phases. For many point-group embeddings, at least once in every finite-group basis of SO3, an extra phase choice arises in the 3jm calculation. The authors show that choosing this phase corresponds to choosing the orientation of the symmetry axes of the groups.