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The running of Newton's constant can be taken into account by consideringcovariant, non local generalizations of the field equations of generalrelativity. These generalizations involve nonanalytic functions of thed'Alembertian, as $(-\Box)^{-\alpha}$, with $\alpha$ a non integer number, and$\ln[-\Box]$. In this paper we define these non local operators in terms of theusual two point function of a massive field. We analyze some of theirproperties, and present specific calculations in flat and Robertson Walkerspacetimes.Comment: 16 pages, no figures. Introduction improved. References added.  Version to appear in Phys. Rev.

Running of Newton’s constant and noninteger powers of the d’Alembertian