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Ponzano-Regge model revisited II: Equivalence with Chern-Simons
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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.
Forward citations
Cited by 2 Pith papers
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UV/IR mixing as an artifact of non-covariant quantisation
UV/IR mixing in noncommutative scalar field theories is shown to be an artifact of a non-covariant quantization choice rather than an intrinsic feature of noncommutativity.
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Les Houches lectures on Spinfoam Path Integrals
A pedagogical review of spinfoam path integrals, from 1d quantum mechanics and 2d BF theory through Ponzano-Regge/Turaev-Viro to the 4d EPRL model, accurate but with no new results.
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