THE CANONICAL CONNECTION IN QUANTUM-MECHANICS

In this paper we investigate the form of induced gauge fields that ari ses in two types of quantum systems. In the first we consider quantum mechanics on coset spaces G/H, and argue that G invariance is central to the emergence of the H connection as induced gauge fields in the di fferent quantum sectors. We then demonstrate why the same connection, now giving rise to the non-Abelian generalization of Berry's phase, ca n also be found in systems that have slow variables taking values in s uch a coset space. (C) 1996 American Institute of Physics.