2004/10/28 by Laurent Freidel, Freidel, Laurent, David Louapre +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #gr-qc #hep-th #math.QA
paper · pdf · doi:10.48550/arxiv.gr-qc/0410141
27 + 23 pages, many figures
arxiv created 2005/02/14 · arxiv updated 2009/12/01
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.