Spin-foam models and the physical scalar product

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

DOI:https://doi.org/10.1103/PHYSREVD.78.104009· OSTI ID:21250910

Alesci, Emanuele ^[1]; Noui, Karim ^[2]; Sardelli, Francesco ^[2]

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1. Laboratoirede Physique, ENS Lyon, CNRS UMR 5672, 46 Allee d'Italie, 69007 Lyon (France)
2. Laboratoire de Mathematiques et de Physique Theorique, Parc de Grammont, 37200 Tours (France)

This paper aims at clarifying the link between loop quantum gravity and spin-foam models in four dimensions. Starting from the canonical framework, we construct an operator P acting on the space of cylindrical functions Cyl({gamma}), where {gamma} is the four-simplex graph, such that its matrix elements are, up to some normalization factors, the vertex amplitude of spin-foam models. The spin-foam models we are considering are the topological model, the Barrett-Crane model, and the Engle-Pereira-Rovelli model. If one of these spin-foam models provides a covariant quantization of gravity, then the associated operator P should be the so-called ''projector'' into physical states and its matrix elements should give the physical scalar product. We discuss the possibility to extend the action of P to any cylindrical functions on the space manifold.

• OSTI ID: 21250910
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 78; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
CYLINDRICAL CONFIGURATION
FOUR-DIMENSIONAL CALCULATIONS
GRAVITATION
MATRIX ELEMENTS
QUANTIZATION
QUANTUM GRAVITY
QUANTUM OPERATORS
SCALARS
SIMULATION
SPACE
SPIN