  The Hamiltonian describing a conductor surrounding an external magnetic field
contains a nonvanishing vector potential in the volume accessible to the
electrons and nuclei of which the conductor is made. That vector potential
cannot be removed by a gauge transformation. Nevertheless, a macroscopic normal
conductor can experience no Aharonov-Bohm effect. That is proved by assuming
only that a normal conductor lacks off-diagonal long-range order (ODLRO). Then
by restricting the Hilbert space to density matrices which lack ODLRO, it is
possible to introduce a restricted gauge transformation that removes the
interaction of the conductor with the vector potential.
