Recent Results Regarding Affine Quantum Gravity
  Recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non-classical modification of the ground state wave function leads to a result that eliminates term-by-term divergences that arise in a conventional perturbation analysis. After a brief review of both the scalar field story and the affine quantum gravity program, examination of the procedures used in the latter surprisingly shows an analogous formulation which already implies that affine quantum gravity is not plagued by divergences that arise in a standard perturbation study. Additionally, guided by the projection operator method to deal with quantum constraints, trial reproducing kernels are introduced that satisfy the diffeomorphism constraints. Furthermore, it is argued that the trial reproducing kernels for the diffeomorphism constraints may also satisfy the Hamiltonian constraint as well. 
John R. Klauder
gr-qc hep-th math-ph math.MP