Spin foam model from canonical quantization

Journal Article · Tue Jan 15 04:00:00 EST 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.77.024009· OSTI ID:21035832

Alexandrov, Sergei ^[1]

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1. Laboratoire de Physique Theorique and Astroparticules, Universite Montpellier II, 34095 Montpellier Cedex 05 (France)

We suggest a modification of the Barrett-Crane spin foam model of four-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 Barrett-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the B field (bivectors) 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 the Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barrett-Crane model.

• OSTI ID: 21035832
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 Vol. 77; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
COMPARATIVE EVALUATIONS
FOUR-DIMENSIONAL CALCULATIONS
GENERAL RELATIVITY THEORY
HILBERT SPACE
LORENTZ INVARIANCE
MODIFICATIONS
QUANTIZATION
QUANTUM GRAVITY
SPIN