Cosmological Deformation of Lorentzian Spin Foam Models

Abstract

We study the quantum deformation of the Barrett-Crane Lorentzian spin foam model which is conjectured to be the discretization of Lorentzian Plebanski model with positive cosmological constant and includes therefore as a particular sector quantum gravity in de-Sitter space. This spin foam model is constructed using harmonic analysis on the quantum Lorentz group. The evaluation of simple spin networks are shown to be non commutative integrals over the quantum hyperboloid defined as a pile of fuzzy spheres. We show that the introduction of the cosmological constant removes all the infrared divergences: for any fixed triangulation, the integration over the area variables is finite for a large class of normalization of the amplitude of the edges and of the faces.

37 pages, 7 figures included

References in corpus (8)

• Spin Foam Models for Quantum Gravity
• Diffeomorphisms and spin foam models
• Quantum gravity with a positive cosmological constant
• Asymptotics of Relativistic Spin Networks
• Asymptotics of 6j and 10j symbols
• Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity
• Non-perturbative summation over 3D discrete topologies
• 6j symbols for U_q(sl_2) and non-Euclidean tetrahedra

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