Dynamical Meaning of Quantum Adiabatic Phase: The Case of a Noncanonical System

Abstract

A dynamical meaning is given for the phase $\Gamma$ recently found in a quantum adiabatic process. A noncanonical system, specifically a spin system coupled with a proper intrinsic system, is considered by use of a path integral in a SU (2) coherent-state representation. It is shown that $\Gamma$ appears as an addition of topological nature to the conventional action function, which leads to a novel form of the semiclassical quantization rule including the phase $\Gamma$.