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2007

A remark on quantum gravity

Kreimer, Dirk

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We discuss the structure of Dyson--Schwinger equations in quantum gravity and conclude in particular that all relevant skeletons are of first order in the loop number.

There is an accompanying sub Hopf algebra on gravity amplitudes equivalent to identities between n-graviton scattering amplitudes which generalize the Slavnov Taylor identities.
These identities map the infinite number of charges and finite numbers of skeletons in gravity to an infinite number of skeletons and a finite number of charges needing renormalization.
Our analysis suggests that gravity, regarded as a probability conserving but perturbatively non-renormalizable theory, is renormalizable after all, thanks to the structure of its Dyson--Schwinger equations.

A remark on quantum gravity · Around

Built on

J. D. Bjorken and S. D. Drell, Relativistic Quantum Field Theory. (German Translation),
1967
Earlier work this paper cites.
B. S. DeWitt, Quantum theory of gravity. II. The manifestly covariant theory,
1967
Earlier work this paper cites.
W. Celmaster and R. J. Gonsalves, The Renormalization Prescription Dependence Of The QCD Coupling Constant,
1979
Earlier work this paper cites.
D. J. Broadhurst, R. Delbourgo and D. Kreimer, Unknotting the polarized vacuum of quenched QED,
1996
Earlier work this paper cites.

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Then

D. Kreimer and K. Yeats, An etude in non-linear Dyson-Schwinger equations,
2006
Later among the works it cites.
C. Bergbauer and D. Kreimer, Hopf algebras in renormalization theory: Locality and Dyson-Schwinger equations from Hochschild cohomology,
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D. Kreimer, Dyson–Schwinger Equations: From Hopf algebras to Number Theory
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