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We derive a model of quantum-classical hybrids for a simplified model ofquantum electrodynamics in the framework of the stochastic variational method.In this model, charged particle trajectories are affected by the interactionwith quantized electromagnetic fields, and this quantum-classical interactioninduces a displacement current. We further investigate a geometric phase in thewave functional of the gauge field configuration, which is induced by adiabaticmotions of the charged particles. This phase contains the quantum-classicalbackreaction effect and usual Berry's phase is reproduced in the vanishinglimit of the fluctuation of the charged particle trajectories.

Quantum-classical hybrids in a simplified model of QED and geometric phase induced by charged particle trajectory