Orthodox quantization of Einstein's gravity: might its unrenormalizability be technically fathomable and physically innocuous?

TL;DR

This paper discusses the nonanalytic nature of quantum gravity in G, its implications for renormalizability, and suggests that classical gravity coupled with quantized fields might be a practical approach due to the smallness of hG.

Contribution

It proposes that the nonrenormalizability of quantum gravity is a consequence of nonanalyticity in G and advocates for a semiclassical approach coupling classical gravity with quantized matter fields.

Findings

Quantum gravity amplitudes are nonanalytic in G at G=0.

Perturbation expansions in G are divergent and unrenormalizable.

Classical gravity treatment is sufficient due to the smallness of hG.

Abstract

Many physical constants related to quantized gravity, e.g., the Planck length, mass, curvature, stress-energy, etc., are nonanalytic in G at G=0, and thus have expansions in powers of G whose terms are progressively more divergent with increasing order. Since the gravity field's classical action is inversely proportional to G, the path integral for gravity-field quantum transition amplitudes shows that these depend on G only through the product hG, and are nonanalytic in G at G=0 for the same reason that all quantum transition amplitudes are nonanalytic in h at h=0, namely their standard oscillatory essential singularity at the classical "limit". Thus perturbation expansions in powers of G of gravity-field transition amplitudes are also progressively more divergent with increasing order, and hence unrenormalizable. While their perturbative treatment is impossible, the exceedingly small value of hG makes the semiclassical treatment of these amplitudes extraordinarily accurate, indeed to such an extent that purely classical treatment of the gravity field ought to always be entirely adequate. It should therefore be fruitful to couple classical gravity to other fields which actually need to be quantized: those fields' ubiquitous, annoying ultraviolet divergences would thereupon undergo drastic self-gravitational red shift, and thus be cut off.