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Article Dans Une Revue Classical and Quantum Gravity Année : 2012

Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory

Résumé

We study the large-j asymptotics of the Euclidean EPRL/FK spin foam amplitude on a 4d simplicial complex with arbitrary number of simplices. We show that for a critical configuration (j_f, g_{ve}, n_{ef}) in general, there exists a partition of the simplicial complex into three regions: Non-degenerate region, Type-A degenerate region and Type-B degenerate region. On both the non-degenerate and Type-A degenerate regions, the critical configuration implies a non-degenerate Euclidean geometry, while on the Type-B degenerate region, the critical configuration implies a vector geometry. Furthermore we can split the Non-degenerate and Type-A regions into sub-complexes according to the sign of Euclidean oriented 4-simplex volume. On each sub-complex, the spin foam amplitude at critical configuration gives a Regge action that contains a sign factor sgn(V_4(v)) of the oriented 4-simplices volume. Therefore the Regge action reproduced here can be viewed as a discretized Palatini action with on-shell connection. The asymptotic formula of the spin foam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries.

Dates et versions

hal-00964087 , version 1 (24-03-2014)

Identifiants

Citer

Muxin Han, Mingyi Zhang. Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory. Classical and Quantum Gravity, 2012, 29 (16), pp.165004. ⟨10.1088/0264-9381/29/16/165004⟩. ⟨hal-00964087⟩
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