ABSTRACT
This chapter begins with quantum R2-gravity and presents the results for gut models with conformai gravity since this is, in principle, a good way of trying to formulate a realistic theory. The attractive features of higher-derivative quantum gravity lead to the attempt to use this theory as the possible basis for a unified theory of all the fundamental interactions. Since the af phenomenon is investigated with the help of renor - malization group equations then it is natural to choose for the description of gravitational interactions a model which leads to a multiplicatively renormalizable quantum theory and admits a renormalization group analysis. The expressions for the counterterms in conformai quantum gravity are determined, just as in the general theory, with the aid of formula. The discovery of the af phenomenon by Gross and Wilczek, and Politzer has stimulated numerous investigations of the renor- malization group equations in the theory of Yang-Mills fields coupled with scalar and spinor fields.
