Geometric phase for cyclic motions and the quantum state space metric

Abstract

The geometric phase is generalized to a cyclic motion resulting from any one-parameter family of transformations in the Hilbert space. This is applied to the translation in one spatial dimension of the Bloch wave function. Physical meanings are given to the Fubini-Study metric on the projective Hilbert space, and a metric in the classical phase space is deduced as the classical limit of this quantum metric. © 1990.