Berry's phase for compact Lie groups

E. Strahov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

The methods of Kähler geometry are applied to generalize the results of Berry obtained for SU(2) (namely, the existence of a geometrical part in the adiabatic phase) to any compact Lie group. We obtain explicit expressions for Berry's geometric phases, Berry's connections, and Berry's curvatures in terms of parameters of the corresponding Lie algebra valued Hamiltonian. It is demonstrated that the parameter space of the Hamiltonian in the general theory is essentially a homogeneous Kahler manifold. The fundamental Kahler potentials of this manifold completely determine Berry's phase. A general approach is exemplified by the Lie algebra Hamiltonians corresponding to SU(2) and SU(3) evolution groups.

Original languageAmerican English
Pages (from-to)2008-2022
Number of pages15
JournalJournal of Mathematical Physics
Volume42
Issue number5
DOIs
StatePublished - May 2001
Externally publishedYes

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