Three-point phase, symplectic measure, and Berry phase
- Cite this article as:
- Cantoni, V. & Mistrangioli, L. Int J Theor Phys (1992) 31: 937. doi:10.1007/BF00675086
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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 state space.