Berry, Simon, and Aharonov and Anandan have discovered, interpreted, and generalized a geometrical phase factor that occurs for a quantum state evolving around a closed path in the projective Hilbert space of rays. Here this phase is directly given in terms of the holonomies of several natural geometrical structures on the projective space.

• Received 10 February 1987

DOI:https://doi.org/10.1103/PhysRevA.36.3479