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
J J Miau et al 1996 Fluid Dyn. Res. 17 311
Roland Schilling 1997 Class. Quantum Grav. 14 1513
J M Hartmann et al 2000 Semicond. Sci. Technol. 15 362
P A Payne 1991 Clin. Phys. Physiol. Meas. 12 105
Andrea Quadri 2004 J. Phys. G: Nucl. Part. Phys. 30 677
L Bombelli et al 1992 J. Phys. A: Math. Gen. 25 1309
S G Allen 1991 J. Radiol. Prot. 11 49
W Edwards and Co. Ltd. 1949 J. Sci. Instrum. 26 129
M A Furman 2006 New J. Phys. 8 279