Gauge theory in the adiabatic approximation

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Abstract
I apply the Born-Oppenheimer approximation to a gauge theory and show how to reconcile it with gauge invariance. Wave functionals used in the adiabatic approximation necessarily break gauge invariance, but this symmetry can be restored after exploiting a novel local symmetry related to transformations of the Berry phase. I then give sufficient conditions for gauge invariance of the adiabatic approximation for the Hamiltonian. As an example I construct a (3+1)-dimensional Abelian theory with unusual propagation characteristics, corresponding to one gauge-invariant ‘‘massive’’ and one ‘‘massless’’ mode.