  We discuss two possible covariant generalizations of the Aharonov-Bohm effect
- one expression in terms of the space-time line integral of the four-vector
potential and the other expression in terms of the space-time "area" integral
of the electric and magnetic fields written in terms of the Faraday 2-form.
These expressions allow one to calculate the Aharonov-Bohm effect for
time-dependent situations. In particular, we use these expressions to study the
case of an infinite solenoid with a time varying flux and find that the phase
shift is zero due to a cancellation of the Aharonov-Bohm phase shift with a
phase shift coming from the Lorentz force associated with the electric field,
${\bf E} = - \partial_t {\bf A}$, outside the solenoid. This result may already
have been confirmed experimentally.
