  In the original setting of the Aharonov-Bohm, the gauge invariant physical
longitudinal mode of the vector potential, which is written by the gauge
invariant physical current $(-e)\bar{\psi}{\boldsymbol \gamma} \psi$, gives the
desired contribution to the Aharonov-Bohm effect. While the scalar mode of the
vector potential, which changes under the gauge transformation so that it is
the unphysical mode, give no contribution to the Aharonov-Bohm effect. Then
Aharonov-Bohm effect really occurs by the physical longitudinal mode in the
original Aharonov-Bohm's setting. In the setting of Tonomura {\it et al.},
where the magnet is shielded with the superconducting material, not only the
magnetic field but also the longitudinal mode of the vector potential become
massive by the Meissner effect. Then not only the magnetic field but also the
physical longitudinal mode does not come out to the region where the electron
travels. In such setting, only the scalar mode of the vector potential exists
in the region where the electron travels, but there is no contribution to the
Aharonov-Bohm effect from that mode. Then, theoretically, the Aharonov-Bohm
effect does not occur in the Tonomura {\it et al.}'s setting. In the quantum
theory, the electron is treated as the wave, and the longitudinal mode give the
change of the phase, which gives the Aharonov-Bohm effect. In the classical
theory, the electron is treated as the particle, and the only existing
longitudinal mode gives the change of the angular momentum. For the particle,
there is no concept of the phase, so that there is no Aharonov-Bohm effect.
