1995/03/27 by R. Loll
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Connection (principal bundle) #Cosmology and Gravitation Theories #Equivalence (formal languages) #Equivalence principle (geometric) #General relativity #Geometry #Loop quantum gravity #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Observable #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Riemann hypothesis #Riemann surface #Theoretical physics #gr-qc #hep-th
paper · pdf · doi:10.1063/1.531253
published as J.Math.Phys.36:6494-6509,1995 · 24 pages, TeX, Mar 95; contribution to the JMP special issue on "Quantum geometry and diffeomorphism invariant quantum field theory"
arxiv created 1995/03/27 · openalex publication_date 1995/11/01 · arxiv updated 2010/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We review and systematize several recent attempts to canonically quantize general relativity in 2+1 dimensions, defined on space–times R×Σg, where Σg is a compact Riemann surface of genus g. The emphasis is on quantizations of the classical connection formulation, which use Wilson loops as their basic observables, but results from the ADM formulation are also summarized. We evaluate the progress and discuss the possible quantum (in)equivalence of the various approaches.