Spin foam model from canonical quantization

Details Spin foam model from canonical quantization Spin foam model from canonical quantization

2007-05-26

arxiv.org/abs/0705.3892v3

Phys.Rev.D77:024009,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages; presentation improved, important changes concerning the closure constraint and the vertex amplitude; minor correctio

Scientific paper

10.1103/PhysRevD.77.024009

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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