Derivation of the geometrical phase
- 1 February 1991
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 43 (3) , 1206-1210
- https://doi.org/10.1103/physreva.43.1206
Abstract
The geometric (Berry) phase is shown to have its origin in the nontrivial geometry of the fiber bundle: Hilbert space→space of states. The nontrivial geometry comes simply from the scalar product in Hilbert space. A comprehensive treatment of the geometrical phase is presented, bringing together the various ideas in the literature.Keywords
This publication has 11 references indexed in Scilit:
- Comment on Geometric Phases for Classical Field TheoriesPhysical Review Letters, 1988
- General Setting for Berry's PhasePhysical Review Letters, 1988
- Geometrical description of Berry's phasePhysical Review A, 1987
- Phase change during a cyclic quantum evolutionPhysical Review Letters, 1987
- Appearance of Gauge Structure in Simple Dynamical SystemsPhysical Review Letters, 1984
- Quantal phase factors accompanying adiabatic changesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1984
- Holonomy, the Quantum Adiabatic Theorem, and Berry's PhasePhysical Review Letters, 1983
- Gravitation, gauge theories and differential geometryPhysics Reports, 1980
- On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nucleiThe Journal of Chemical Physics, 1979
- Intersection of potential energy surfaces in polyatomic moleculesDiscussions of the Faraday Society, 1963