Spin foam models of Riemannian quantum gravity

John C Baez, J Daniel Christensen, Thomas R Halford, David C Tsang

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

Using numerical calculations, we compare three versions of the Barrett-Crane model of four-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 given by 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.
Original languageEnglish
Pages (from-to)4627-4648
Number of pages22
JournalClassical Quantum Gravity
Volume19
Issue number18
DOIs
Publication statusPublished - 21 Aug 2002

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