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Spin Foam Diagrammatics and Topological Invariance

Florian Girelli·Robert Oeckl·Alejandro Perez
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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.

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Florian Girelli, Robert Oeckl, Alejandro Perez. 2001-11-07. Spin Foam Diagrammatics and Topological Invariance. https://doi.org/10.1088/0264-9381%2F19%2F6%2F305

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