Finiteness and dual variables for Lorentzian spin foam models

@article{Cherrington2006FinitenessAD,
  title={Finiteness and dual variables for Lorentzian spin foam models},
  author={Janelle Cherrington},
  journal={Classical and Quantum Gravity},
  year={2006},
  volume={23},
  pages={701-719}
}
  • J. Cherrington
  • Published 20 August 2005
  • Mathematics
  • Classical and Quantum Gravity
We describe here some new results concerning the Lorentzian Barrett–Crane model, a well-known spin foam formulation of quantum gravity. Generalizing an existing finiteness result, we provide a concise proof of finiteness of the partition function associated with all non-degenerate triangulations of 4-manifolds and for a class of degenerate triangulations not previously shown. This is accomplished by a suitable re-factoring and re-ordering of integration, through which a large set of variables… 
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    We give a short and simple proof that the Lorentzian 10j symbol, which forms a key part of the Barrett–Crane model of Lorentzian quantum gravity, is finite. The argument is very general, and applies
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    Positivity in Lorentzian Barrett–Crane models of quantum gravity
    The Barrett–Crane models of Lorentzian quantum gravity are a family of spin foam models based on the Lorentz group. We show that for various choices of edge and face amplitudes, including the
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    We present a spin foam formulation of Lorentzian quantum general relativity. The theory is based on a simple generalization of a Euclidean model defined in terms of a field theory over a group. The
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    The partition function of the SO(4)- or Spin(4)-symmetric Euclidean Barrett–Crane model can be understood as the sum over all quantized geometries of a given triangulation of a four-manifold. In the
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