A confined magnetic field punctures the configuration space of a charged particle, producing the Aharonov-Bohm phase shift through the resulting change in topology.
Therefore, the charged particle responds only to the modified topology of its configuration space, which is R2 − { 0}
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Magnetic flux and its topological effects in Aharonov-Bohm effect
A confined magnetic field punctures the configuration space of a charged particle, producing the Aharonov-Bohm phase shift through the resulting change in topology.