Quantum Gravity as a Broken Symmetry Phase of a BF Theory

We explain how General Relativity with a cosmological constant arises as a broken symmetry phase of a BF theory. In particular we show how to treat de Sitter and anti-de Sitter cases simultaneously. This is then used to formulate a quantisation of General Relativity through a spin foam perturbation theory. We then briefly discuss how to calculate the effective action in this quantization procedure.Comment: This is a contribution to the Proc. of the O'Raifeartaigh Symposium on Non-Perturbative and Symmetry Methods in Field Theory (June 2006, Budapest, Hungary), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Solution to the Cosmological Constant Problem in a Regge Quantum Gravity Model

We show that it is possible to solve the cosmological constant (CC) problem in a discrete quantum gravity theory based on Regge calculus by using the effective action approach and a special path-integral measure. The effective cosmological constant is given as a sum of 3 terms: the classical CC, the quantum gravity CC and the matter CC. Since the observations can only measure the sum of these 3 terms, we can choose the classical CC to be equal to the negative value of the matter CC. Hence the effective CC is given only by the quantum gravity CC, which is determined by the path-integral measure. Since the path-integral measure depends on a free parameter, this parameter can be chosen such that the effective CC gives the observed value.Comment: v4: published version. arXiv admin note: substantial text overlap with arXiv:1407.112