Effective Action for Adiabatic Process: Dynamical Meaning of Berry and Simon's Phase

Abstract

By applying the path integral method to two interacting systems, it is shown that the specific phase Γ appearing in the quantum adiabatic process recently found by Berry and Simon is obtained as an additive action to the conventional dynamical action function. This scheme naturally gives a dynamical meaning to Berry and Simon’s topological phase, which leads to a novel form of semiclassical quantization rule including the phase Γ.