Generalized affine coherent states: A natural framework for the quantization of metric-like variables

Affine variables, which have the virtue of preserving the positive-definite character of matrix-like objects, have been suggested as replacements for the canonical variables of standard quantization schemes, especially in the context of quantum gravity. We develop the kinematics of such variables, d iscussing suitable coherent states, their associated resolution of unity, p olarizations, and finally the realization of the coherent-state overlap fun ction in terms of suitable path-integral formulations. (C) 2000 American In stitute of Physics. [S0022-2488(00)03807-X].