2010/06/10 by You Ding, Carlo Rovelli
Mathematics · Medicine · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Classical mechanics #Covariant transformation #Euclidean quantum gravity #Group field theory #Hilbert space #Immirzi parameter #Loop quantum gravity #Mathematical analysis #Mathematical physics #Mathematics #Neuroblastoma Research and Treatments #Noncommutative and Quantum Gravity Theories #Operator (biology) #POVM #Physics #Quantum #Quantum dynamics #Quantum geometry #Quantum gravity #Quantum mechanics #Quantum process #Spin (aerodynamics) #Spin foam #Spin network #Theoretical physics #gr-qc
paper · pdf · doi:10.1088/0264-9381/27/20/205003
published as Class.Quant.Grav.27:205003,2010 · 11 pages
arxiv created 2010/06/10 · openalex publication_date 2010/09/07 · arxiv updated 2014/11/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract\nA covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In this paper we reconsider the implementation of the constraints that defines the model. We define in a simple way the boundary Hilbert space of the theory, introducing a slight modification of the embedding of the SU (2) representations into the SL(2, C) ones. We then show directly that all constraints vanish on this space in a weak sense. The vanishing is exact (and not just in the large quantum number limit.) We also generalize the definition of the volume operator in the spinfoam model to the Lorentzian signature, and show that it matches the one of loop quantum gravity, as does in the Euclidean case.