A remark on quantum gravity
arXiv:0705.3897 · doi:10.1016/j.aop.2007.06.005
Abstract
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.
9p, several eps figures
References in corpus (10)
- Nonperturbative Evolution Equation for Quantum Gravity
- On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
- Ultraviolet Fixed Point and Generalized Flow Equation of Quantum Gravity
- Renormalization in quantum field theory and the Riemann-Hilbert problem II: the -function, diffeomorphisms and the renormalization group
- String-Based Methods in Perturbative Gravity
- Exact solutions of Dyson-Schwinger equations for iterated one-loop integrals and propagator-coupling duality
- Perturbative Gravity from QCD Amplitudes
- An Étude in non-linear Dyson--Schwinger Equations
- Anatomy of a gauge theory
- Unknotting the polarized vacuum of quenched QED
Cited by in corpus (12)
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- Algebraic structures in quantum gravity
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- Gravity-Matter Feynman Rules for any Valence
- Diffeomorphisms of quantum fields
- Not so non-renormalizable gravity
- Gauge Symmetries and Renormalization
- Perturbative Gravity in the Causal Approach
- Renormalization in combinatorially non-local field theories: the Hopf algebra of 2-graphs
- Field diffeomorphisms and the algebraic structure of perturbative expansions
- Algebraic Structures in the Coupling of Gravity to Gauge Theories
- New Approach to GUTs