Events in a Non-Commutative Space-Time

Details Events in a Non-Commutative Space-Time Events in a Non-Commutative Space-Time

2003-05-14

arxiv.org/abs/hep-th/0305121v2

Phys.Rev.D70:024006,2004

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, revtex. Introductory part shortened and some arguments made more clear

Scientific paper

10.1103/PhysRevD.70.024006

We treat the events determined by a quantum physical state in a noncommutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operator-valued 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 coordinate observables and discuss the covariance of the model under the Poincare' group. The unusual transformation law of the coordinates under space-time translations is interpreted as a failure of the absolute character of the concept of space-time coincidence. The model shows that a minimal length is compatible with Lorents covariance.

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