### [1003.5680] A dynamical classification of the range of pair

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**April 21 2010**This nice paper (unfortunately not crossposted to astro-ph) studies the well-definedness of classical interactions which go like a power-law in the long-range limit, in [tex]d[/tex] dimensions. Newtonian gravity in three dimensions is a particular marginally pathological case. The fact that Newtonian gravity is not well-defined for an infinite system is of course well known in cosmology, but this puts the problem nicely in context. (It would be interesting to know what are the statistical properties of similar systems in general relativity, where there is no problem with infinite systems and the physics is quite different.)

As a minor issue, the authors also argue that systems where the absolute force diverges can be considered well-defined is the relative forces between particles remain finite, which seems to me odd, since absolute acceleration is measurable.

As a minor issue, the authors also argue that systems where the absolute force diverges can be considered well-defined is the relative forces between particles remain finite, which seems to me odd, since absolute acceleration is measurable.