Three-point phase, symplectic measure, and Berry phase

  title={Three-point phase, symplectic measure, and Berry phase},
  author={Vittorio Cantoni and L. Mistrangioli},
  journal={International Journal of Theoretical Physics},
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… 
1 Citations

The geometric phase and ray space isometries

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



Geometrical description of Berry's phase.

  • Page
  • Mathematics
    Physical review. A, General physics
  • 1987
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

Phase change during a cyclic quantum evolution.

A new geometric phase factor is defined for any cyclic evolution of a quantum system. This is independent of the phase factor relating the initial and final state vectors and the Hamiltonian, for a

Quantal phase factors accompanying adiabatic changes

  • M. Berry
  • Physics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1984
A quantal system in an eigenstate, slowly transported round a circuit C by varying parameters R in its Hamiltonian Ĥ(R), will acquire a geometrical phase factor exp{iγ(C)} in addition to the familiar

Perturbative induction of vector potentials.

Degenerate perturbation theory, without geometrical tools, directly yields vector potentials in the Born-Oppenheimer approximation. The derivation uses only the algebra of the dynamical operators,

Geometry of quantum evolution.

It is shown that the integral of the uncertainty of energy with respect to time is independent of the particular Hamiltonian used to transport the quantum system along a given curve in the projective Hilbert space, which gives a new time-energy uncertainty principle.