Spin Foam Perturbation Theory for Three-Dimensional Quantum Gravity |
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Authors: | Jo?o?Faria?Martins Aleksandar?Mikovi? |
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Institution: | (1) Centro de Matemática da Universidade do Porto, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007 Porto, Portugal;(2) Departamento de Matemática, Universidade Lusófona de Humanidades e Tecnologia, Av do Campo Grande, 376, 1749-024 Lisboa, Portugal |
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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.
Member of the Mathematical Physics Group, University of Lisbon. |
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