1992/06/26 by Steven Carlip · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmological constant #Cosmology and Gravitation Theories #Euclidean geometry #Euclidean quantum gravity #Euclidean space #Geometry #Lambda #Limit (mathematics) #Loop quantum gravity #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Partition function (quantum field theory) #Path integral formulation #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Sign (mathematics) #Spacetime #Spin foam #Theoretical physics #hep-th
paper · pdf · doi:10.1088/0264-9381/10/2/004
published as Class.Quant.Grav.10:207-218,1993 · 12 pages (LaTeX), UCD-92-16
arxiv created 1992/06/26 · openalex publication_date 1993/02/01 · arxiv updated 2010/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In 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.