RENORMALIZATION-GROUP AND EFFECTIVE POTENTIAL IN HIGHER-DERIVATIVE QUANTUM-GRAVITY WITH MATTER

A general formalism for studying the one-loop and renormalization grou p (RG) improved potential (in linear curvature approximation) in a mul tiplicatively renormalizable theory of matter with quantum R2-gravity is presented. The phenomenon of dimensional transmutation, which leads to the definition of a scalar coupling constant in terms of gravitati onal couplings, is discussed in the examples of the f(phi)4 theory and scalar QED. The RG improved potential in the f(phi)4 theory is found. It is shown that the stability of this potential can be influenced by quantum gravity (QG) effects. The QG corrections to scalar-to-vector mass ratio are found in scalar electrodynamics.