## Orthodox Quantization of Einstein's Gravity: Might Its Unrenormalizability be Technically Fathomable and Physically Innocuous?

**Authors:** Steven Kenneth Kauffmann

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 ℏG, and are nonanalytic in G at G = 0 for the same reason
that all quantum transition amplitudes are nonanalytic in ℏ at ℏ = 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 ℏG 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.

**Comments:** 6 pages, Also archived as arXiv:0908.3024 [physics.gen-ph]. Conclusion section added.

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### Submission history

[v1] 2 Dec 2009

[v2] 1 Oct 2010

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