2011/05/31 by Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn · 6 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Canonical quantum gravity #Classical mechanics #Cosmology and Gravitation Theories #Diffeomorphism #General relativity #Hamiltonian (control theory) #Hamiltonian constraint #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Phase space #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Spacetime #String theory #Supergravity #Supersymmetry #Theoretical physics #Wheeler–DeWitt equation #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/30/4/045001
published as Class. Quantum Grav. 30 (2013) 045001 · 28 pages. v2: Journal version. Minor clarifications
openalex publication_date 2013/01/23 · arxiv created 2013/02/12 · arxiv updated 2013/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Loop Quantum Gravity heavily relies on a connection formulation of General Relativity such that 1. the connection Poisson commutes with itself and 2. the corresponding gauge group is compact. This can be achieved starting from the Palatini or Holst action when imposing the time gauge. Unfortunately, this method is restricted to D+1 = 4 spacetime dimensions. However, interesting String theories and Supergravity theories require higher dimensions and it would therefore be desirable to have higher dimensional Supergravity loop quantisations at one's disposal in order to compare these approaches. In this series of papers, we take first steps towards this goal. The present first paper develops a classical canonical platform for a higher dimensional connection formulation of the purely gravitational sector. The new ingredient is a different extension of the ADM phase space than the one used in LQG, which does not require the time gauge and which generalises to any dimension D > 1. The result is a Yang-Mills theory phase space subject to Gauss, spatial diffeomorphism and Hamiltonian constraint as well as one additional constraint, called the simplicity constraint. The structure group can be chosen to be SO(1,D) or SO(D+1) and the latter choice is preferred for purposes of quantisation.