Simple spin networks as Feynman graphs

1999/03/31 by Laurent Freidel, L. Freidel, Kirill Krasnov +1 · 9 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th #math-ph #math.MP

paper · pdf · doi:10.1063/1.533203

published as J.Math.Phys. 41 (2000) 1681-1690 · 13 pages, no figures; few typos corrected

arxiv created 1999/06/17 · openalex publication_date 2000/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show how spin networks can be described and evaluated as Feynman integrals over an internal space. This description can, in particular, be applied to the so-called simple SO(D) spin networks that are of importance for higher-dimensional generalizations of loop quantum gravity. As an illustration of the power of the new formalism, we use it to obtain the asymptotics of an amplitude for the D simplex and show that its oscillatory part is given by the Regge action.

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