2009/01/13 by Herbert W. Hamber · 1 citation
Physics and Astronomy · #Asymptotic safety in quantum gravity #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Euclidean quantum gravity #Functional renormalization group #Infrared fixed point #Lattice (music) #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Quantum gravity #Renormalization #Renormalization group #gr-qc #hep-th
paper · pdf · doi:10.1007/s10714-009-0769-y
published as Gen.Rel.Grav.41:817-876,2009 · 63 pages, 12 figures
arxiv created 2009/01/13 · openalex publication_date 2009/02/07 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other non-renormalizable theories, I discuss the general methods and goals of the lattice approach. An underlying theme is the attempt at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation theory, and the recent lattice results, which apply to the strong gravity regime and are inherently non-perturbative. A second theme in this review is the ever-present natural correspondence between infrared methods of strongly coupled non-abelian gauge theories on the one hand, and the low energy approach to quantum gravity based on the renormalization group and universality of critical behavior on the other. Towards the end of the review I discuss possible observational consequences of path integral quantum gravity, as derived from the non-trivial ultraviolet fixed point scenario. I argue that the theoretical framework naturally leads to considering a weakly scale-dependent Newton’s constant, with a scaling violation parameter related to the observed scaled cosmological constant (and not, as naively expected, to the Planck length).