Scaling behavior of interacting quantum fields in curved spacetime

Abstract

We propose a version of the 't Hooft-Weinberg renormalization-group equation which is valid in general curved spacetimes. The key idea is to regard the Green's functions as functions of the metric and to scale the metric rather than the coordinates or momenta. We apply these equations to the infrared limit of the effective conformal coupling in $\lambda {\phi }^4$ theory.