2011/05/31 by Norbert Bodendorfer, Thomas Thiemann, Andreas Thurn · 8 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Connection (principal bundle) #Constraint (computer-aided design) #Cosmology and Gravitation Theories #Diagonal #General relativity #Geometry #Linear-quadratic-Gaussian control #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Optimal control #Physics #Quantum #Quantum gravity #Quantum mechanics #Spin foam #Spin network #Theoretical physics #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/30/4/045003
published as Class. Quantum Grav. 30 (2013) 045003 · 36 pages. v2: Journal version. Discussion on simplicity constraints extended. Conclusion and outlook extended. Minor clarifications
openalex publication_date 2013/01/23 · arxiv created 2013/02/12 · arxiv updated 2013/02/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We quantise the new connection formulation of D+1 dimensional General Relativity developed in our companion papers by Loop Quantum Gravity (LQG) methods. It turns out that all the tools prepared for LQG straightforwardly generalise to the new connection formulation in higher dimensions. The only new challenge is the simplicity constraint. While its "diagonal" components acting at edges of spin network functions are easily solved, its "off-diagonal" components acting at vertices are non trivial and require a more elaborate treatment.