Spin Foam Perturbation Theory for Three-Dimensional Quantum Gravity

Abstract

We formulate the spin foam perturbation theory for three-dimensional Euclidean Quantum Gravity with a cosmological constant. We analyse the perturbative expansion of the partition function in the dilute-gas limit and we argue that the Baez conjecture stating that the number of possible distinct topological classes of perturbative configurations is finite for the set of all triangulations of a manifold, is not true. However, the conjecture is true for a special class of triangulations which are based on subdivisions of certain 3-manifold cubulations. In this case we calculate the partition function and show that the dilute-gas correction vanishes for the simplest choice of the volume operator. By slightly modifying the dilute-gas limit, we obtain a nonvanishing correction which is related to the second order perturbative correction. By assuming that the dilute-gas limit coupling constant is a function of the cosmological constant, we obtain a value for the partition function which is independent of the choice of the volume operator.

Revised version. We prove that the first-order volume expectation value vanishes and therefore we consider a dilute gas limit based on the second-order perturbative correction. 32 pages, 16 Figures

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• Observables in the Turaev-Viro and Crane-Yetter models
• Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model
• Quantum Gravity as a Deformed Topological Quantum Field Theory
• Invariants of Spin Networks Embedded in Three-Manifolds
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Cited by in corpus (2)

• Investigation of the Spinfoam Path integral with Quantum Cuboid Intertwiners
• Anisotropic Spinfoam Cosmology