2011/04/28 by Etera R. Livine, Daniele Oriti, James P. Ryan
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Covariant Hamiltonian field theory #Covariant transformation #Hamiltonian (control theory) #Hamiltonian constraint #Hamiltonian system #Immirzi parameter #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #Physics #Quantum #Quantum gravity #Quantum mechanics #Renormalization group #Spin foam #Spin network #Theoretical physics #gr-qc
paper · pdf · doi:10.1088/0264-9381/28/24/245010
published as Class. Quantum Grav. 28 (2011) 245010 · 14 pages
arxiv created 2011/04/28 · openalex publication_date 2011/11/29 · arxiv updated 2015/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Spinfoam models provide a covariant formulation of the dynamics of loop quantum gravity. They are non-perturbatively defined in the group field theory (GFT) framework; the GFT partition function defines the sum of spinfoam transition amplitudes over all possible (discretized) geometries and topologies. The issue remains, however, of explicitly relating the specific form of the GFT action and the canonical Hamiltonian constraint. Here, we suggest an avenue for addressing this issue. Our strategy is to expand GFTs around non-trivial classical solutions and to interpret the induced quadratic kinematical term as defining a Hamiltonian constraint on the group field and thus on spin-network wavefunctions. We apply our procedure to Boulatov GFT for 3D Riemannian gravity. Finally, we discuss the relevance of understanding the spectrum of this Hamiltonian operator for the renormalization of GFTs.