Spinfoam 2d quantum gravity and discrete bundles

Details Spinfoam 2d quantum gravity and discrete bundles Spinfoam 2d quantum gravity and discrete bundles

2004-06-15

arxiv.org/abs/gr-qc/0406063v2

Class.Quant.Grav. 22 (2005) 85-108

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages, 3 figures. Comments added, to appear in Class.Quant.Grav

Scientific paper

10.1088/0264-9381/22/1/006

In 4 dimensions, general relativity can be formulated as a constrained $BF$ theory; we show that the same is true in 2 dimensions. We describe a spinfoam quantization of this constrained BF-formulation of 2d riemannian general relativity, obtained using the Barrett-Crane technique of imposing the constraint as a restriction on the representations summed over. We obtain the expected partition function, thus providing support for the viability of the technique. The result requires the nontrivial topology of the bundle where the gravitational connection is defined, to be taken into account. For this purpose, we study the definition of a principal bundle over a simplicial base space. The model sheds light also on several other features of spinfoam quantum gravity: the reality of the partition function; the geometrical interpretation of the Newton constant, and the issue of possible finiteness of the partition function of quantum general relativity.

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