1993/10/08 by John W. Barrett, J. W. Barrett, Timothy J. Foxon +1 · 66 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Euclidean quantum gravity #Group field theory #Homotopy and Cohomology in Algebraic Topology #Loop quantum gravity #Mathematical physics #Noncommutative and Quantum Gravity Theories #Path integral formulation #Physics #Pure mathematics #Quantum #Quantum dynamics #Quantum geometry #Quantum gravity #Quantum mechanics #Quantum process #Semiclassical gravity #Semiclassical physics #Simplicial manifold #Simplicial set #Spin foam #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/11/3/009
published in Classical and Quantum Gravity 11(3), 543-556 (IOP Publishing) · 14 pages in Plain TeX, (figures available on request), DAMTP-R93/26
arxiv created 1993/10/08 · openalex publication_date 1994/03/01 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
We consider the simplicial state sum model of Ponzano and Regge as a path integral for quantum gravity in three dimensions. We examine the Lorentzian geometry of a single 3-simplex and of a simplicial manifold, and interpret an asymptotic formula for 6j-symbols in terms of this geometry. This extends Ponzano and Regge's similar interpretation for Euclidian geometry. We give a geometric interpretation of the stationary points of this state sum, by showing that, at these points, the simplicial manifold may be mapped locally into flat Lorentzian or Euclidian space. This lends weight to the interpretation of the state sum as a path integral, which has solutions corresponding to both Lorentzian and Euclidian gravity in three dimensions.