Three-point phase, symplectic measure, and Berry phase

@article{Cantoni1992ThreepointPS,
  title={Three-point phase, symplectic measure, and Berry phase},
  author={Vittorio Cantoni and L. Mistrangioli},
  journal={International Journal of Theoretical Physics},
  year={1992},
  volume={31},
  pages={937-943}
}
It is shown that the geometric phase (Berry phase) around a cycle in the complex projective space of pure states of a quantum mechanical system can be expressed in terms of an elementary three-point phase function which is the simplest manifestation of the complexity of the underlying Hilbert space. In terms of this three-point phase it is possible to construct a geometrically relevant phase function defined mod 4π on the cycles and closely related to the natural symplectic structure of the… 
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