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

TL;DR

This paper reformulates spin-foam models as quantum field theories of spin networks, introducing matter spin foam models that incorporate matter fields and have potential applications in quantum gravity and topological quantum field theories.

Contribution

It introduces a new class of matter spin foam models derived from a quantum field theory of spin networks, extending the framework to include matter fields and dual face-edge labeling.

Findings

New matter spin foam models formulated for open spin networks

Models incorporate face and edge labels from tensor categories

Potential applications in quantum gravity and topological QFTs

Abstract

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.