Quantum Field Theory of Open Spin Networks and New Spin Foam Models

Details Quantum Field Theory of Open Spin Networks and New Spin Foam Models Quantum Field Theory of Open Spin Networks and New Spin Foam Models

2002-02-07

arxiv.org/abs/gr-qc/0202026v1

Int.J.Mod.Phys.A18S2:83-96,2003

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, based on the talk given at the X-th Oporto Meeting on Geometry, Physics and Topology, Porto, September 20-24, 2001

Scientific paper

10.1142/S0217751X0301797X

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.

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