Events in a noncommutative space-time

We treat the events determined by a quantum physical state in a non-commutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operatorvalued measures (POVMs). We consider in detail the model proposed by Snyder in 1947 and calculate the POVMs defined on the real line that describe the measurement of a single coordinate. The approximate joint measurement of all the four space-time coordinates is described in terms of a generalized Wigner function (GWF). We derive lower bounds for the dispersion of the coordi