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Affine quantum gravity involves (i) affine commutation relations to ensuremetric positivity, (ii) a regularized projection operator procedure toaccomodate first- and second-class quantum constraints, and (iii) a hard-coreinterpretation of nonlinear interactions to understand and potentially overcomenonrenormalizability. In this program, some of the less traditionalmathematical methods employed are (i) coherent state representations, (ii)reproducing kernel Hilbert spaces, and (iii) functional integralrepresentations involving a continuous-time regularization. Of specialimportance is the profoundly different integration measure used for theLagrange multiplier (shift and lapse) functions. These various concepts arefirst introduced on elementary systems to help motivate their application toaffine quantum gravity.Comment: 15 pages, Presented at the X-International Conference on Symmetry  Methods in Physic

The utility of coherent states and other mathematical methods in the foundations of affine quantum gravity