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

D. López Nacir, F. D. Mazzitelli
2007 Physical Review D  
The running of Newton's constant can be taken into account by considering covariant, non local generalizations of the field equations of general relativity. These generalizations involve nonanalytic functions of the d'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 the usual two point function of a massive field. We analyze some of their properties, and present specific calculations in flat
more » ... lculations in flat and Robertson Walker spacetimes.
doi:10.1103/physrevd.75.024003 fatcat:l7dqzwhribhkbkawvusa5fkmpy