  In this article it will be presented the first attempt made in order to
perform gauge invariant calculations of eigenstates of a quantum body in its
condensed phase, the latter reacting to an external uniform magnetic field. The
target is achieved introducing a new unitary translation operator transforming
eigenstates into a new set of eigenstates having different total linear
momentum. This new quantum representation solves the problem of calculating the
magnetic response of quantum eigenstates of finite or either infinite periodic
systems to uniform magnetic fields, where equivalence between the customarily
used representation and the new representation has been made.
