  Generalized solutions of the standard gauge transformation equations are
presented and discussed in physical terms. They go beyond the usual Dirac phase
factors and they exhibit nonlocal quantal behavior, with the well-known
Relativistic Causality of classical fields affecting directly the phases of
wavefunctions in the Schroedinger Picture. These nonlocal phase behaviors,
apparently overlooked in path-integral approaches, give a natural account of
the dynamical nonlocality character of the various (even static) Aharonov-Bohm
phenomena, while at the same time they seem to respect Causality. Indeed, for
particles passing through nonvanishing magnetic or electric fields they lead to
cancellations of Aharonov-Bohm phases at the observation point, generalizing
earlier semiclassical experimental observations (of Werner & Brill) to
delocalized (spread-out) quantum states. This leads to a correction of
previously unnoticed sign-errors in the literature, and to a natural
explanation of the deeper reason why certain time-dependent semiclassical
arguments are consistent with static results in purely quantal Aharonov-Bohm
configurations. These nonlocalities also provide a remedy for misleading
results propagating in the literature (concerning an uncritical use of Dirac
phase factors, that persists since the time of Feynman's work on path
integrals). They are shown to conspire in such a way as to exactly cancel the
instantaneous Aharonov-Bohm phase and recover Relativistic Causality in earlier
"paradoxes" (such as the van Kampen thought-experiment), and to also complete
Peshkin's discussion of the electric Aharonov-Bohm effect in a causal manner.
The present formulation offers a direct way to address time-dependent single-
vs double-slit experiments and the associated causal issues -- issues that have
recently attracted attention, with respect to the inability of current theories
to address them.
