Spin Foam Diagrammatics and Topological Invariance

Abstract

We provide a simple proof of the topological invariance of the Turaev-Viro model (corresponding to simplicial 3d pure Euclidean gravity with cosmological constant) by means of a novel diagrammatic formulation of the state sum models for quantum BF-theories. Moreover, we prove the invariance under more general conditions allowing the state sum to be defined on arbitrary cellular decompositions of the underlying manifold. Invariance is governed by a set of identities corresponding to local gluing and rearrangement of cells in the complex. Due to the fully algebraic nature of these identities our results extend to a vast class of quantum groups. The techniques introduced here could be relevant for investigating the scaling properties of non-topological state sums, being proposed as models of quantum gravity in 4d, under refinement of the cellular decomposition.

20 pages, latex with AMS macros and eps figures

References in corpus (2)

• Generalized Lattice Gauge Theory, Spin Foams and State Sum Invariants
• The Quantum Geometry of Supersymmetry and the Generalized Group Extension Problem

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