2012/10/25 by Madhavan Varadarajan · 1 citation
Mathematics · Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Covariance #Covariant transformation #Diffeomorphism #General covariance #Gravitation #Hamiltonian (control theory) #Hamiltonian constraint #Lie algebra #Loop quantum gravity #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Poisson bracket #Quantum #Quantum gravity #Quantum mechanics #Wheeler–DeWitt equation #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.87.044040
published as Phys.Rev. D87 (2013) 4, 044040 · 56 pages, No figures
arxiv created 2012/10/25 · openalex publication_date 2013/02/19 · arxiv updated 2015/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The GNewton\ensuremath→0 limit of Euclidean gravity introduced by Smolin is described by a generally covariant U(1)3 gauge theory. In an earlier paper, Tomlin and Varadarajan constructed the quantum Hamiltonian constraint of density weight 4/3 for this U(1)3 theory so as to produce a nontrivial anomaly-free loop quantum gravity type representation of the Poisson bracket between a pair of Hamiltonian constraints. These constructions involved a choice of regulating coordinate patches. The use of these coordinate patches is in apparent conflict with spatial diffeomorphism covariance. In this work we show how an appropriate choice of coordinate patches together with suitable modifications of these constructions results in the diffeomorphism covariance of the continuum limit action of the Hamiltonian constraint operator, while preserving the anomaly-free property of the continuum limit action of its commutator.