Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-10-14
Class.Quant.Grav.25:085011,2008
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
48 pages, 4 figures, RevTeX, one reference added
Scientific paper
10.1088/0264-9381/25/8/085011
Group Field Theories, a generalization of matrix models for 2d gravity, represent a 2nd quantization of both loop quantum gravity and simplicial quantum gravity. In this paper, we construct a new class of Group Field Theory models, for any choice of spacetime dimension and signature, whose Feynman amplitudes are given by path integrals for clearly identified discrete gravity actions, in 1st order variables. In the 3-dimensional case, the corresponding discrete action is that of 1st order Regge calculus for gravity (generalized to include higher order corrections), while in higher dimensions, they correspond to a discrete BF theory (again, generalized to higher order) with an imposed orientation restriction on hinge volumes, similar to that characterizing discrete gravity. The new models shed also light on the large distance or semi-classical approximation of spin foam models. This new class of group field theories may represent a concrete unifying framework for loop quantum gravity and simplicial quantum gravity approaches.
Oriti Daniele
Tlas Tamer
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