The induced non-Abelian gauge structure of the effective Hamiltonian arising from the Born-Oppenheimer approximation is investigated. It is shown that the trace of the electric part of the gauge potential is related to the natural metric on the complex Grassmannian of Hilbert subspaces. Our results are illustrated by a simple example yielding SU(2) gauge fields (instantons), and the corresponding electric gauge potential. The latter gives a contribution to the induced effective scalar potential. Electric gauge potentials associated with higher-dimensional monopoles are also obtained. For systems exhibiting such gauge structure it is shown that the sign of the effective scalar potential depends on the Abelian or non-Abelian character of the gauge group.
ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics