REALIZATION OF BERRYS PHASE AND HANNAYS ANGLE THROUGH CANONICAL-TRANSFORMATIONS

A new relationship between Berry's phase and Hannay's angle (which is its classical counterpart) is established. This relationship is exact and does not depend on semiclassical arguments, though in this note th e aforementioned relationship is proved only for a restricted class of Hamiltonians. It is shown that if a Hamiltonian, for which Berry's ph ase and Hannay's angle are nonvanishing, can, in classical theory, be canonically transformed into one for which both are zero, the generati ng function of this canonical transformation yields, through appropria te averages, both the quantal geometrical phase and its classical anal og.