2002/02/07 by Aleksandar Miković, A. Mikovic · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Bundle #Cosmology and Gravitation Theories #Fiber bundle #Group field theory #Loop quantum gravity #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantization (signal processing) #Quantum #Quantum field theory #Quantum gravity #Quantum mechanics #Spin (aerodynamics) #Spin foam #Spin network #Theoretical physics #Topological quantum field theory #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1142/s0217751x0301797x
published as Int.J.Mod.Phys.A18S2:83-96,2003 · 13 pages, based on the talk given at the X-th Oporto Meeting on Geometry, Physics and Topology, Porto, September 20-24, 2001
arxiv created 2002/02/07 · openalex publication_date 2003/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We describe how a spin-foam state sum model can be reformulated as a quantum field theory of spin networks, such that the Feynman diagrams of that field theory are the spin-foam amplitudes. In the case of open spin networks, we obtain a new type of state-sum models, which we call the matter spin foam models. In this type of state-sum models, one labels both the faces and the edges of the dual two-complex for a manifold triangulation with the simple objects from a tensor category. In the case of Lie groups, such a model corresponds to a quantization of a theory whose fields are the principal bundle connection and the sections of the associated vector bundles. We briefly discuss the relevance of the matter spin foam models for quantum gravity and for topological quantum field theories.