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Affine variables, which have the virtue of preserving the positive-definitecharacter of matrix-like objects, have been suggested as replacements for thecanonical variables of standard quantization schemes, especially in the contextof quantum gravity. We develop the kinematics of such variables, discussingsuitable coherent states, their associated resolution of unity, polarizations,and finally the realization of the coherent-state overlap function in terms ofsuitable path-integral formulations.Comment: 17 pages, LaTeX, no figure

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