Noncanonical quantization of gravity. II. Constraints and the physical Hilbert space

The program of quantizing the gravitational field with the help of affine f ield variables is continued. For completeness, a review of the selection cr iteria that singles out the affine fields, the alternative treatment of con straints, and the choice of the initial (before imposition of the constrain ts) ultralocal representation of the field operators is initially presented . As analogous examples demonstrate, the introduction and enforcement of th e gravitational constraints will cause sufficient changes in the operator r epresentations so that all vestiges of the initial ultralocal field operato r representation disappear. To achieve this introduction and enforcement of the constraints, a well characterized phase space functional integral repr esentation for the reproducing kernel of a suitably regularized physical Hi lbert space is developed and extensively analyzed. (C) 2001 American Instit ute of Physics.