Recent Results Regarding Affine Quantum Gravity

TL;DR

This paper discusses recent progress in affine quantum gravity, highlighting how non-classical modifications and the projection operator method can address divergences and satisfy quantum constraints.

Contribution

It introduces a novel approach using trial reproducing kernels to satisfy diffeomorphism and Hamiltonian constraints in affine quantum gravity.

Findings

Affine quantum gravity may avoid divergences similar to nonrenormalizable scalar fields.

Trial reproducing kernels can satisfy quantum constraints.

The approach suggests a divergence-free formulation of quantum gravity.

Abstract

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.