2002/10/28 by Thomas Thiemann · 26 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1007/978-3-540-45230-0_3
published as Lect.Notes Phys.631:41-135,2003 · 90 pages, Latex, 18 figures, uses graphicx and pstricks for coloured text and graphics, based on lectures given at the 271st WE Heraeus Seminar ``Aspects of Quantum Gravity: From Theory to Experimental Search'', Bad Honnef, Germany, February 25th -- March 1st, to appear in Lecture Notes in Physics
arxiv created 2002/10/28 · openalex publication_date 2003/01/01 · arxiv updated 2015/06/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
Quantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured over the past fifteen years to a mathematically rigorous candidate quantum field theory of the gravitational field. The features that distinguish it from other quantum gravity theories are 1) background independence and 2) minimality of structures. Background independence means that this is a non-perturbative approach in which one does not perturb around a given, distinguished, classical background metric, rather arbitrary fluctuations are allowed, thus precisely encoding the quantum version of Einstein's radical perception that gravity is geometry. Minimality here means that one explores the logical consequences of bringing together the two fundamental principles of modern physics, namely general covariance and quantum theory, without adding any experimentally unverified additional structures. The approach is purposely conservative in order to systematically derive which basic principles of physics have to be given up and must be replaced by more fundamental ones. QGR unifies all presently known interactions in a new sense by quantum mechanically implementing their common symmetry group, the four-dimensional diffeomorphism group, which is almost completely broken in perturbative approaches. These lectures offer a problem -- supported introduction to the subject.