2002/11/30 by Laurent Freidel, David Louapre · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Combinatorics #Computer science #Context (archaeology) #Field (mathematics) #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Loop quantum gravity #Mathematics #Network topology #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Spin network #Theoretical physics #Topological quantum field theory #Topology (electrical circuits) #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.68.104004
published as Phys.Rev. D68 (2003) 104004 · 20 pages, 9 figures, note added, minor corrections
arxiv created 2002/12/10 · openalex publication_date 2003/11/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The group field theories realizing the sum over all triangulations of all topologies of 3D discrete gravity amplitudes are known to be nonuniquely Borel summable. We modify these models to construct a new group field theory which is proved to be uniquely Borel summable, defining in an unambiguous way a nonperturbative sum over topologies in the context of 3D dynamical triangulations and spin foam models. Moreover, we give some arguments to support the fact that, despite our modification, this new model is similar to the original one, and therefore could be taken as a definition of the sum over topologies of 3D quantum gravity amplitudes.