# 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…

## One Citation

### The geometric phase and ray space isometries

- Mathematics
- 1997

We study the behaviour of the geometric phase under isometries of the ray space. This leads to a better understanding of a theorem first proved by Wigner: isometries of the ray space can always be…

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