The Nonlocality of Topological Quantum Phases
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.
Aharonov Y, Cohen E, & Rohrlich, D. The nonlocality of topological quantum phases. arXiv preprint arXiv:1502.05716, 2015.