The Nonlocality of Topological Quantum Phases

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Aharonov, Yakir; Cohen, Eliahu; Rohrlich, Daniel
nonlocality; electromagnetic; scalar potentials; vector potentials; local interactions; gauge-invariant; gauge-dependent; quantum phases; Quantum Physics
article description
Are the electromagnetic scalar and vector potentials dispensable? Lev Vaidman has suggested that local interactions of gauge-invariant quantities, e.g. magnetic torques, suffice for the description of all quantum electromagnetic phenomena. We analyze a selection of thought experiments that challenge this suggestion. All of them have explanations in terms of local interactions of gauge-dependent quantities; in addition, some have explanations in terms of nonlocal interactions of gauge-invariant quantities. We claim, however, that two of our examples have no gauge-invariant explanation and that electromagnetic potentials are, in general, truly indispensable.