Affine Quantum Gravity

A sketch of the affine quantum gravity program illustrates a different perspective on several difficult issues of principle: metric positivity; quantum anomalies; and nonrenormalizability. Quantum gravity is under study from several viewpoints. Brane world scenarios and loop quantum gravity represent the two most popular approaches [1], yet alternative viewpoints may also deserve consideration. One such alternative — called affine quantum gravity — rests on just a few basic principles, outlined below. First, we recall some hurdles that any approach to quantum gravity must face. Our list of problems that must be faced is short, but each problem is major. These problems are: (1) maintaining the physical nature of the metric field; (2) dealing with a set of open first-class classical constraints that becomes partially second class on quantization; and (3) overcoming the perturbative nonrenormalizability of conventional quantum gravity (i.e., Einstein’s theory, to which we confine our attention). Affine quantum gravity looks at these major problems from a fresh perspective [2]. What follows is a brief overview of this program. This essay received an “honorable mention” in the 2003 Essay Competition of the Gravity Research Foundation. Electronic mail: [email protected]