Recent results regarding affine quantum gravity (Q2872253)

Affine quantum gravity is a program for quantization of the Einstein gravitational field in four-dimensional spacetime that differs in many respects from the approach taken in string theory or in loop quantum gravity. The usual problems encountered in quantizing gravity such as: nonrenormalizability, enforcing the gravitational constraints, etc., arise in affine quantum gravity as well, and some of these issues have already been discussed in the two principal papers on this subject.NEWLINENEWLINERecent 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.