2005/01/31 by Hermann Nicolai, Kasper Peeters, Marija Zamaklar · 6 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/22/19/r01
published as Class.Quant.Grav.22:R193,2005 · 57 pages, 11 figures; v2: substantially revised, references added, resubmitted to Class. Quant. Grav.; v3: further substantial improvements; v4: small changes, final version to appear in Class. Quant. Grav
arxiv created 2005/09/18 · openalex publication_date 2005/09/21 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasize that the off-shell ('strong') closure of the constraint algebra is a crucial test of quantum spacetime covariance, and thereby of the consistency, of the theory. Special attention is paid to the appearance of a large number of ambiguities, in particular in the formulation of the Hamiltonian constraint. Developing suitable approximation methods to establish a connection with classical gravity on the one hand, and with the physics of elementary particles on the other, remains a major challenge.