Active versus passive transformations in the presence of a magnetic field

G. F. Torres del Castillo, D. A. Rosete-Álvarez

Published 2016-03-04Version 1

It is shown that, when there is a magnetic field present, in the framework of classical or quantum mechanics, the active translations differ from the passive ones and that the canonical momentum is not the generator of them. It is also shown that an infinitesimal generator of passive translations or rotations exists only if the magnetic field is invariant under these transformations.