  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, discussing
suitable coherent states, their associated resolution of unity, polarizations,
and finally the realization of the coherent-state overlap function in terms of
suitable path-integral formulations.
