Spin foam model from canonical quantization

Abstract : We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide a generalization of the unique Barrette-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the $B$ field (bi-vectors) should be promoted not to generators of the gauge algebra, but to their certain projection. The modification is also justified by the canonical analysis of Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barret-Crane model.
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http://hal.in2p3.fr/in2p3-00152760
Contributor : Francoise Duceau <>
Submitted on : Thursday, June 7, 2007 - 3:20:24 PM
Last modification on : Tuesday, November 19, 2019 - 9:08:02 PM

Citation

Sergei Alexandrov. Spin foam model from canonical quantization. Physical Review D, American Physical Society, 2007, 77, pp.024009. ⟨10.1103/PhysRevD.77.024009⟩. ⟨in2p3-00152760⟩

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