N ov 2 00 4 Attractions of Affine Quantum Gravity ∗

All attempts to quantize gravity face several difficult problems. Among these problems are: (i) metric positivity (positivity of the spatial distance between distinct points), (ii) the presence of anomalies (partial second-class nature of the quantum constraints), and (iii) perturbative nonrenormalizability (the need for infinitely many distinct counterterms). In this report, a relatively nontechnical discussion is presented about how the program of affine quantum gravity proposes to deal with these problems. Introduction and Survey The program of affine quantum gravity differs from that of string theory or loop quantum gravity: specifically, it differs in the insistence on a spatial metric tensor that is strictly positive definite; in the simultaneous and uniform treatment of both firstand second-class operator constraints; in dealing with nonperturbative renormalizability; and in maintaining a close connection with the motivating classical (Einstein) gravity theory. A suitable realization of these principles is most readily presented within a formalism that is, for the most part, generally unfamiliar to many readers. The purpose of this paper is to provide a relatively simple introduction to several concepts used to study quantum gravity from this new perspective. Presented at the Sixth Intl. Symp. on the Frontiers of Fund. Physics, Udine, Italy, Sept., 2004 Electronic mail: [email protected]