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Maxwell duality, Lorentz invariance, and topological phase. (English) Zbl 0958.81017
Summary: We discuss the Maxwell electromagnetic duality relations between the Aharonov-Bohm, Aharonov-Casher, and He-McKellar-Wilkens topological phases, which allow a unified description of all three phenomena. We also elucidate Lorentz transformations which allow these effects to be understood in an intuitive fashion in the rest frame of the moving quantum particle. Finally, we propose two experimental schemes for measuring the He-McKellar-Wilkens phase.

MSC:
81Q70 Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory
81P15 Quantum measurement theory, state operations, state preparations
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