Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Invariant Berry connections

Luc Vinet

Published Apr 15, 1988• 37 citations

Abstract

Berry connections are shown to be invariant under the action of symmetry groups on parameter space. This observation allows one to use the theory of invariant Yang-Mills potentials to evaluate these connections without computing the instantaneous energy eigenstates. Hamiltonians belonging to the algebra of a Lie group are examined in this light. They provide a wide class of systems admitting nontrivial adiabatic holonomy. The special case of the generalized harmonic oscillator is analyzed and the SO(2,1) invariance of the associated Berry connection is exhibited.

DOI: 10.1103/physrevd.37.2369

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