GEOMETRIC PHASES FOR SU(3) REPRESENTATIONS AND 3 LEVEL QUANTUM-SYSTEMS

A comprehensive analysis of the pattern of geometric phases arising in unitary representations of the group SU(3) is presented. The structur e of the group manifold, convenient local coordinate systems and their overlaps, and complete expressions for the Maurer-Cartan forms are de scribed. Combined with a listing of all inequivalent continuous subgro ups of SU(3) and the general properties of dynamical phases associated with Lie group unitary representations, one finds that nontrivial dyn amical phases arise only in three essentially different situations. Th e case of three level quantum systems, which is one of them, is examin ed in further detail and a generalization of the SU(3) solid angle for mula is developed. (C) 1997 Academic Press