We show that the standard Dirac phase factor is not the only solution of thegauge transformation equations. The full form of a general gauge function (thatconnects systems that move in different sets of scalar and vector potentials),apart from Dirac phases also contains terms of classical fields that actnonlocally (in spacetime) on the local solutions of the time-dependentSchr\"odinger equation: the phases of wavefunctions in the Schr\"odingerpicture are affected nonlocally by spatially and temporally remote magnetic andelectric fields, in ways that are fully explored. These contributions go beyondthe usual Aharonov-Bohm effects (magnetic or electric). (i) Application tocases of particles passing through static magnetic or electric fields leads tocancellations of Aharonov-Bohm phases at the observation point; these arelinked to behaviors at the semiclassical level (to the old Werner & Brillexperimental observations, or their "electric analogs" - or to recent reportsof Batelaan & Tonomura) but are shown to be far more general (true not only fornarrow wavepackets but also for completely delocalized quantum states). Byusing these cancellations, certain previously unnoticed sign-errors in theliterature are corrected. (ii) Application to time-dependent situationsprovides a remedy for erroneous results in the literature (on improper uses ofDirac phase factors) and leads to phases that contain an Aharonov-Bohm part anda field-nonlocal part: their competition is shown to recover RelativisticCausality in earlier "paradoxes" (such as the van Kampen thought-experiment),while a more general consideration indicates that the temporal nonlocalitiesfound here demonstrate in part a causal propagation of phases of quantummechanical wavefunctions in the Schr\"odinger picture. This may open a directway to address time-dependent double-slit experiments and the associated causalissues
展开▼
