S Carlip 1993 Class. Quantum Grav. 10 207 doi:10.1088/0264-9381/10/2/004
S Carlip
Show affiliationsIn the Euclidean path-integral approach to quantum gravity, the partition function for Hawking's 'volume canonical ensemble' is computed by summing contributions from all possible topologies. The behaviour such a sum can be estimated in three spacetime dimensions in the limit of small cosmological constant. The sum over topologies diverges for any sign of Lambda , but for dramatically different reasons: for Lambda )0, the divergent behaviour comes from the contributions of very low-volume, topologically complex manifolds, while for Lambda )0 it is a consequence of the existence of infinite sequences of relatively high-volume manifolds with converging geometries. Possible implications for four-dimensional quantum gravity are discussed.
Issue 2 (February 1993)
S Carlip 1993 Class. Quantum Grav. 10 207
D V Ahluwalia-Khalilova 2005 Class. Quantum Grav. 22 1433
Lorenzo Iorio 2003 Class. Quantum Grav. 20 L5
K Wette et al 2008 Class. Quantum Grav. 25 235011
Murat Durandurdu 2009 J. Phys.: Condens. Matter 21 452204
G B Andresen et al 2008 J. Phys. B: At. Mol. Opt. Phys. 41 011001
Paul A Blaga and Cristina Blaga 2001 Class. Quantum Grav. 18 3893
Bruno Bellomo et al 2007 J. Phys. A: Math. Theor. 40 9437
Johnathon R Walls et al 2007 Phys. Med. Biol. 52 2775
Abhay Ashtekar and Jerzy Lewandowski 2004 Class. Quantum Grav. 21 R53