  The ideal scalar Aharonov-Bohm (SAB) and Aharonov-Casher (AC) effect involve
a magnetic dipole pointing in a certain fixed direction: along a purely time
dependent magnetic field in the SAB case and perpendicular to a planar static
electric field in the AC case. We extend these effects to arbitrary direction
of the magnetic dipole. The precise conditions for having nondispersive
precession and interference effects in these generalized set ups are delineated
both classically and quantally. Under these conditions the dipole is affected
by a nonvanishing torque that causes pure precession around the directions
defined by the ideal set ups. It is shown that the precession angles are in the
quantal case linearly related to the ideal phase differences, and that the
nonideal phase differences are nonlinearly related to the ideal phase
differences. It is argued that the latter nonlinearity is due the appearance of
a geometric phase associated with the nontrivial spin path. It is further
demonstrated that the spatial force vanishes in all cases except in the
classical treatment of the nonideal AC set up, where the occurring force has to
be compensated by the experimental arrangement. Finally, for a closed
space-time loop the local precession effects can be inferred from the
interference pattern characterized by the nonideal phase differences and the
visibilities. It is argued that this makes it natural to regard SAB and AC as
essentially local and nontopological effects.
