  Affine coherent states are generated by affine kinematical variables much
like canonical coherent states are generated by canonical kinematical
variables. Although all classical and quantum formalisms normally entail
canonical variables, it is shown that affine variables can serve equally well
for many classical and quantum studies. This general purpose analysis provides
tools to discuss two major applications: (1) the completely successful
quantization of a nonrenormalizable scalar quantum field theory by affine
techniques, in complete contrast to canonical techniques which only offer
triviality; and (2) a formulation of the kinematical portion of quantum gravity
that favors affine kinematical variables over canonical kinematical variables,
and which generates a framework in which a favorable analysis of the
constrained dynamical issues can take place. All this is possible because of
the close connection between the affine and the canonical stories, while the
few distinctions can be used to advantage when appropriate.
