Abstract
The representation theory of the Galilean group extended by a one-dimensional group of dilations (which leave invariant the free Schrodinger equation) is studied. The existence of position and time operators is investigated from the standpoint of the imprimitivity theorem, for quantum particles whose states carry a projective representation of the extended group. Position and time operators are shown to exist for some two-component direct sums with non-trivial multipliers and for vector representations with zero helicity.
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