We point to previously overlooked solutions of the standard gauge transformation equations of Electrodynamics: the generalized "gauge functions" go beyond the usual Dirac phase factors (spatial or temporal integrals of potentials) and exhibit a new form of nonlocal quantal behavior, with the well-known Relativistic Causality of classical fields affecting directly the phases of quantum mechanical wavefunctions. Because of the new solutions, the phases of wavefunctions in the Schrodinger picture are affected nonlocally by spatially and temporally remote magnetic and electric fields, in specific ways that are briefly demonstrated. The new nonlocalities, apparently overlooked in path-integral approaches, compete with Aharonov-Bohm behaviors and they provide: (i) a correction to a number of erroneous results in the literature (either an uncritical use of Dirac phases that persists since the time of Feynman's work on path integrals, or a sign error that still propagates in the literature and that regards the connection of Aharonov-Bohm phases to semiclassical phases picked up inside nonvanishing fields due to path-deflections by the Lorentz force), (ii) a new interpretation of semiclassical observations and further extensions to delocalized states (a "generalized Werner & Brill cancellation"), (iii) a natural remedy of earlier "paradoxes" (such as the van Kampen thought-experiment, as well as Peshkin's discussion of the electric Aharonov-Bohm effect that is made "causal" by the new solutions), and (iv) a new formulation directly applicable to the study of time-dependent slit-experiments and their causal issues.
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