Lectures on Loop Quantum Gravity

By T. Thiemann. 2002

358 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f92912de79ebdb452a20ed974bbda211a43b9cd0

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Citations in the corpus

Brane-World Gravity (2004, neutral): “, [365, 409]).”
Black-hole entropy from quantum geometry (2004, methodology): “A Hilbert space of solutions is constructed via the diffeomorphism averaging procedure whose Quantum Geometry version is well described in [ 1 ,3].”
Quantum foam and topological strings (2003, background): “as quantized in units of gs (for quantization of areas in a different context see e.g., [ 15 ]).”
Inflationary Cosmology in Modified Gravity Theories (2015, methodology): “Particularly, we consider inflation (i) derived by modification terms of gravity [26]; (ii) through the quantum anomaly [27]; and (iii) in R gravity in the framework of the so-called loop quantum cosmology (LQC) [29–33] to include quantum effects [28] (for reviews on LQC, see, for example, [34–40]).”
FUNDAMENTAL STRUCTURE OF LOOP QUANTUM GRAVITY (2005, background): “of many important statements. One may ﬁnd the missing details in the references cited. Thus our review will not be comprehensive. We refer to Ref.[124] for a more detailed exploration, Refs. [17] and [126] for more advanced topics. It turns out that in the framework of loop quantum gravity all theor”
Quantum-Spacetime Phenomenology (2008, methodology): “An example of this type is provided by Loop Quantum Gravity (LQG) [476, 96, 502, 524, 93], where one is presently unable to even formulate many desirable physics questions, but at least some (however tentative) progress has been made [247, 33, 523, 75, 128] in the exploration of the kinematics of th”
The universe from scratch (2005, background): “Progress has undoubtedly been made, at the very least in terms of developing technical tools to describe quantum geometry nonperturbatively (see, for example, [ 11 , 12, 13]).”
Three-dimensional loop quantum gravity: physical scalar product and spin-foam models (2004, background): “Loop quantum gravity aims at characterizing the space of solutions of quantum Einstein’s equations represented, in the canonical framework, by the previous set of constraints (for recent reviews see [2, 3, 4] and the beautifull new book by Rovelli [5]; for an extensive and deep description of the ma”
Reconstructing the universe (2005, background): “For example, this is not yet the case in loop quantum gravity [ 4 , 5, 6] or in four-dimensional spin foam models for gravity [7].”
Loop Quantum Gravity (2003, background): “– Thiemann’s lectures [292] (not to be confused with the book) are a very good and readable straightforward introduction to loop quantum gravity.”