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.
Cite
@article{arxiv.0804.2811,
title = {Spin Foam Perturbation Theory for Three-Dimensional Quantum Gravity},
author = {Joao Faria Martins and Aleksandar Mikovic},
journal= {arXiv preprint arXiv:0804.2811},
year = {2017}
}
Comments
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