2004/10/28 by Laurent Freidel, Freidel, Laurent, David Louapre +1 · 57 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Chern–Simons theory #Computation #Cosmology and Gravitation Theories #Equivalence (formal languages) #FOS: Mathematics #FOS: Physical sciences #Gauge group #Gauge theory #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Observable #Physics #Pure mathematics #Quantization (signal processing) #Quantum Algebra (math.QA) #Quantum mechanics #Theoretical physics #gr-qc #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.gr-qc/0410141
published in arXiv (Cornell University) (Cornell University) · 27 + 23 pages, many figures
openalex publication_date 2004/10/28 · arxiv created 2005/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We provide a mathematical definition of the gauge fixed Ponzano-Regge model showing that it gives a measure on the space of flat connections whose volume is well defined. We then show that the Ponzano-Regge model can be equivalently expressed as Reshetikhin-Turaev evaluation of a colored chain mail link based on D(SU(2)): a non compact quantum group being the Drinfeld double of SU(2) and a deformation of the Poincare algebra. This proves the equivalence between spin foam quantization and Chern-Simons quantization of three dimensional gravity without cosmological constant. We extend this correspondence to the computation of expectation value of physical observables and insertion of particles.