Daniele Oriti et al 2005 Class. Quantum Grav. 22 85 doi:10.1088/0264-9381/22/1/006
Daniele Oriti1, Carlo Rovelli2,3 and Simone Speziale1,3
Show affiliationsIn four dimensions (4D), general relativity (GR) can be formulated as a constrained BF theory; we show that the same is true in 2D. We describe a spinfoam quantization of this constrained BF formulation of 2D Riemannian GR, 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 also sheds light 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 GR.
Issue 1 (7 January 2005)
Received 5 August 2004
Published 3 December 2004
Daniele Oriti et al 2005 Class. Quantum Grav. 22 85
Roy Maartens et al 1997 Class. Quantum Grav. 14 1927
Lorenzo Iorio and Herbert I M Lichtenegger 2005 Class. Quantum Grav. 22 119
S. G. Djorgovski et al. 2003 ApJ 596 67
K Tachibana et al 1984 J. Phys. D: Appl. Phys. 17 1727
Amos Harpaz 2002 Eur. J. Phys. 23 263
T K Yeh et al 2007 Metrologia 44 393
V Damodara Das and K Seetharama Bhat 1989 J. Phys. D: Appl. Phys. 22 162
M R Smith and D G Hughes 1971 J. Phys. E: Sci. Instrum. 4 725
M J Rakovic and Shih-I Chu 1998 J. Phys. B: At. Mol. Opt. Phys. 31 1989