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Affine coherent states are generated by affine kinematical variables muchlike canonical coherent states are generated by canonical kinematicalvariables. Although all classical and quantum formalisms normally entailcanonical variables, it is shown that affine variables can serve equally wellfor many classical and quantum studies. This general purpose analysis providestools to discuss two major applications: (1) the completely successfulquantization of a nonrenormalizable scalar quantum field theory by affinetechniques, in complete contrast to canonical techniques which only offertriviality; and (2) a formulation of the kinematical portion of quantum gravitythat favors affine kinematical variables over canonical kinematical variables,and which generates a framework in which a favorable analysis of theconstrained dynamical issues can take place. All this is possible because ofthe close connection between the affine and the canonical stories, while thefew distinctions can be used to advantage when appropriate.

The Utility of Affine Variables and Affine Coherent States