Lectures on Loop Quantum Gravity

Abstract

AbstractQuantum General Relativity (QGR), sometimes called Loop Quantum Gravity, has matured overthe past fifteen years to a mathematically rigorous candidate quantum field theory of the gravita-tional field. The features that distinguish it from other quantum gravity theories are 1) backgroundindependence and 2) minimality of structures.Background independence means that this is a non-perturbative approach in which one does notperturb around a given, distinguished, classical background metric, rather arbitrary fluctuations areallowed, thus precisely encoding the quantum version of Einstein’s radical perception that gravity isgeometry.Minimality here means that one explores the logical consequences of bringing together the twofundamental principles of modern physics, namely general covariance and quantum theory, withoutadding any experimentally unverified additional structures such as extra dimensions, extra symme-tries or extra particle content beyond the standard model. While this is a very conservative approachand thus maybe not very attractive to many researchers, it has the advantage that pushing the theoryto its logical frontiers will undoubtedly either result in a successful theory or derive exactly whichextra structures are required, if necessary. Or put even more radically, it may show which basicprinciples of physics have to be given up and must be replaced by more fundamental ones.QGR therefore is, by definition, not a unified theory of all interactions in the standard sensesince such a theory would require a new symmetry principle. However, it unifies all presently knowninteractions in a new sense by quantum mechanically implementing their common symmetry group,the four-dimensional diffeomorphism group, which is almost completely broken in perturbative ap-proaches.