Gauge Invariance as a Consequence of Galilei-Invariance for Elementary Particles

If a distinction is made between kinematical and dynamical symmetries of a quantum mechanical localizable system it is possible to extend the principle of Galilei-invariance to elementary particles, subject to arbitrary external forces. This principle implies a severe restriction on the possible types of external forces which can act on a particle. In fact we show in this paper that for a scalar particle the only forces which are compatible with this principle are those which derive from a scalar and vectorpotential. The Hamiltonian takes on the usual gauge-invariant form of a charged particle in interaction with arbitrary electromagnetic forces.