Functional Renormalization Group Equations, Asymptotic Safety, and Quantum Einstein Gravity
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These lecture notes provide a pedagogical introduction to a specific continuum implementation of the Wilsonian renormalization group, the effective average action. Its general properties and, in particular, its functional renormalization group equation are explained in a simple scalar setting. The approach is then applied to Quantum Einstein Gravity (QEG). The possibility of constructing a fundamental theory of quantum gravity in the framework of Asymptotic Safety is discussed and the supporting evidence is summarized.
Based on lectures given by M.R. at the ``First Quantum Geometry and Quantum Gravity School'', Zakopane, Poland, March 2007, and the ``Summer School on Geometric and Topological Methods for Quantum Field Theory'', Villa de Leyva, Colombia, July 2007, and by F.S. at NIKHEF, Amsterdam, The Netherlands, June 2006
Based on lectures given by M.R. at the ``First Quantum Geometry and Quantum Gravity School'', Zakopane, Poland, March 2007, and the ``Summer School on Geometric and Topological Methods for Quantum Field Theory'', Villa de Leyva, Colombia, July 2007, and by F.S. at NIKHEF, Amsterdam, The Netherlands, June 2006