Spin Foam Models of Riemannian Quantum Gravity

Details Spin Foam Models of Riemannian Quantum Gravity Spin Foam Models of Riemannian Quantum Gravity

2002-02-06

arxiv.org/abs/gr-qc/0202017v4

Class.Quant.Grav.19:4627-4648,2002

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages LaTeX; this version to appear in Classical and Quantum Gravity

Scientific paper

10.1088/0264-9381/19/18/301

Using numerical calculations, we compare three versions of the Barrett-Crane model of 4-dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De Pietri, Freidel, Krasnov, and Rovelli, we show the partition function diverges very rapidly for many triangulated 4-manifolds. In the version with modified face and edge amplitudes due to Perez and Rovelli, we show the partition function converges so rapidly that the sum is dominated by spin foams where all the spins labelling faces are zero except for small, widely separated islands of higher spin. We also describe a new version which appears to have a convergent partition function without drastic spin-zero dominance. Finally, after a general discussion of how to extract physics from spin foam models, we discuss the implications of convergence or divergence of the partition function for other aspects of a spin foam model.

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