oscillator*. Such states are the proper quantum version of points; the classical limit of Quantum Spacetime is then the product of Minkowski space and $\Sigma_1$. Thus extradimensions, described by the doubled 2-sphere, are predicted by Quantum Spacetime.

Optimally localized states are central in the definition of the *Quantum Wick Product*, which removes the UV divergences in the Gell-Mann–Low expansion of the S matrix for polynomial interactions on QST  [@BDFP:2003].

The mentioned minimum, of the order of the squared Planck length in generic units, for the sum of the four squared uncertainties in the coordinates of an event is the first manifestation of a deeper fact: the minimum euclidean distance between two independent events in Quantum Spacetime is of the order of the Planck length in all reference frames. More generally, for each geometric operator like distance, area, three volume, or four volume, the sum of the squares of all spacetime components is, in each reference frame, at least of the order of the appropriate power of the Planck length [@BDFP:2011].

These are mathematical results on the Quantum Geometry of Quantum Minkowski space. But dynamics, already at the level of a semiclassical treatment of Gravity, strongly suggests that the minimal distance 