Aharonov-Bohm Effect: Gauge Invariance Consequence

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What is the Aharonov-Bohm effect and why it is a conseguence of the gauge invariance?
 
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The A-B effect is the deflection of a charged particle by the vector potential A in a region where there is no magnetic B field. It shows that GI cannot be purely classical, but must also involve a change in the QM wave function.