Non local aspects of quantum phases

Non local aspects of the geometric, gauge field and gravitational quantum phases are discussed. The geometric phase is generalized to one obtained from a connection with an arbitrary Chern class over the projective Hilbert space. A new geometric interpretation is given to it as an area in the projective Hilbert space, regarded as a phase space, and its relationship to the classical phase space area is pointed out. It is argued that gauge fields provide a fundamental reason for introducing Planck's constant. Remarks are also made on the gravitational quantum phase and its implication to Weyl's theory of gravity