ABSTRACT

In the framework of classical mechanics, the presence of a magnetostatic field implies that a rigid translation or a rotation is a canonical transformation (with respect to the usual symplectic structure) if and only if the magnetic field is invariant under that transformation. In quantum mechanics, in the presence of a magnetostatic field, there are no operators representing those translations or rotations that do not leave invariant the magnetic field and the corresponding components of the linear or angular momentum are undefined.