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The asymptotic safety approach to quantum gravity provides a nonperturbative notion of renormalization in order to find a consistent and predictive quantum field theory of the gravitational interaction and spacetime geometry. It is based upon a nontrivial fixed point of the corresponding renormalization group (RG) flow such that the running coupling constants approach this fixed point in the ultraviolet (UV) limit. This suffices to avoid divergences in physical observables. Moreover, it has predictive power: Generically an arbitrary starting configuration of coupling constants given at some RG scale does not run into the fixed point for increasing scale, but a subset of configurations might have the desired UV properties. For this reason it is possible that — assuming a particular set of couplings has been measured in an experiment — the requirement of asymptotic safety fixes all remaining couplings in such a way that the UV fixed point is approached.
Dynamical dimensional reduction or spontaneous dimensional reduction is the apparent reduction in the number of spacetime dimensions as a function of the distance scale, or conversely the energy scale, with which spacetime is probed. At least within the current level of experimental precision, our universe has three dimensions of space and one of time. However, the idea that the number of dimensions may increase at extremely small length scales was first proposed more than a century ago, and is now fairly commonplace in theoretical physics. Contrary to this, a number of recent results in quantum gravity suggest the opposite behavior, a dynamical reduction of the number of spacetime dimensions at small length scales.
References
- ↑ Wilson, Kenneth G.; Kogut, John B. (1974). "The renormalization group and the ε expansion". Physics Reports. 12 (2): 75–199. Bibcode:1974PhR....12...75W. doi:10.1016/0370-1573(74)90023-4.
- ↑ Zinn-Justin, Jean (2002). Quantum Field Theory and Critical Phenomena. Oxford University Press.
- 1 2 Niedermaier, Max; Reuter, Martin (2006). "The Asymptotic Safety Scenario in Quantum Gravity". Living Rev. Relativ. 9 (1): 5. Bibcode:2006LRR.....9....5N. doi:10.12942/lrr-2006-5. PMC 5256001 . PMID 28179875.
- ↑ Weinberg, Steven (1979). "Ultraviolet divergences in quantum theories of gravitation". In Hawking, S.W.; Israel, W. (eds.). General Relativity: An Einstein centenary survey . Cambridge University Press. pp. 790–831. ISBN 9780521222853.
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