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Abstract

Uniqueness of the Position Observable in an Irreducible Unitary Representation up to a Factor of the Galilei Group.

An elementarary quantum mechanical system with non vanishing mass is characterized by a continuous irreducible unitary representation up to a factor of the Galilei group in Hilbert space. An argument is given concerning the continuous iurreducible unitary representations of the universal covering group of the Euclidean group such that the position observable is uniquely determined by the transformation properties under the representation of the Galilei group.