Unique Euler Angles and Self-Consistent Multiplication Tables for Double Point Groups

摘要

The standard Euler angle parameterization of rotations is to unique. This is a particular problem when considering spinor representations. We enlarge the domain of the Euler angles from an SO_3 covering to an SU_2 covering, 0 <= #alpha# < 2#pi#, 0 <= #beta# <= #pi#, 0 <= #gamma# < 4#pi#. With this modification we can find unique Euler angles for operations of the double groups and thus construct self-consistent group tables for those groups. Factor systems can then be described for the projective representations.