Noncyclic geometric phase and its non-Abelian generalization
- 4 November 1999
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 32 (46) , 8157-8171
- https://doi.org/10.1088/0305-4470/32/46/312
Abstract
We use the theory of dynamical invariants to yield a simple derivation of noncyclic analogues of the Abelian and non-Abelian geometric phases. This derivation relies only on the principle of gauge invariance and elucidates the existing definitions of the Abelian noncyclic geometric phase. We also discuss the adiabatic limit of the noncyclic geometric phase and compute the adiabatic non-Abelian noncyclic geometric phase for a spin-1 magnetic (or electric) quadrupole interacting with a precessing magnetic (electric) field.Keywords
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This publication has 36 references indexed in Scilit:
- Adiabatic Berry Phase and Hannay Angle for Open PathsAnnals of Physics, 1998
- Extending the quantal adiabatic theorem: Geometry of noncyclic motionAmerican Journal of Physics, 1998
- Gauge-invariant reference section and geometric phaseJournal of Physics A: General Physics, 1995
- Quantum Kinematic Approach to the Geometric Phase. I. General FormalismAnnals of Physics, 1993
- On the real and complex geometric phasesProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1992
- Berry's Geometrical Phase for Noncyclic HamiltoniansEurophysics Letters, 1989
- Geometric quantum phase and anglesPhysical Review D, 1988
- General Setting for Berry's PhasePhysical Review Letters, 1988
- Phase change during a cyclic quantum evolutionPhysical Review Letters, 1987
- Quantal phase factors accompanying adiabatic changesProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1984