Spin Foam Diagrammatics and Topological Invariance

Details Spin Foam Diagrammatics and Topological Invariance Spin Foam Diagrammatics and Topological Invariance

2001-11-07

arxiv.org/abs/gr-qc/0111022v1

Class.Quant.Grav. 19 (2002) 1093-1108

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, latex with AMS macros and eps figures

Scientific paper

10.1088/0264-9381/19/6/305

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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