Quantum kinematic approach to the geometric phase. II. The case of unitary group representations

Abstract

The quantum kinematic approach to geometric phases, developed in a preceding paper, is applied to the case of phases arising from unitary representations of Lie groups on Hilbert space. Specific features of this situation are brought out by fully exploiting the (Lie) algebraic and (differential) geometric aspects that are naturally available. Systematic classification of distinct situatians that can arise, simplifications based on the Wigner-Eckart theorem, and existence of gauge type invariances in the expression for the geometric phase, are all explained. Numerous examples illustrating the formalism are presented.