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30 September 2023
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A New Spin Foam Model for 4d Gravity
Laurent Freidel ; Kirill Krasnov ;
Date 13 Aug 2007
AbstractStarting from the Plebanski formulation of gravity as a constrained BF theory we propose a new spin foam model for 4d Riemmanian quantum gravity that generalises the well-known model of Barrett-Crane and resolves the ultralocality problem that this model is known to possess. It is well known that the BF formulation of 4d gravity possesses two sectors: one corresponding to gravity and the other topological. The model presented here is shown to give a quantisation of the gravitational sector. The present model is dual to the recently proposed spin foam model of Engle et al. which, we show, corresponds to the topological sector of the theory. One important outcome of our approach is that it also allow us to introduce the Immirzi parameter into the framework of spin foam quantisation. We generalize some of our considerations to the Lorentzian setting and obtain a new spin foam model in that context as well.
Source arXiv, 0708.1595
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