The hessian in spin foam models

Abstract

We fill one of the remaining gaps in the asymptotic analysis of the vertex amplitudes of the Engle-Pereira-Rovelli-Livine (EPRL) spin foam models: We show that the hessian is nondegenerate for the stationary points that corresponds to geometric nondegenerate $4$ simplices. Our analysis covers the case when all faces are spacelike.

30 pages

References in corpus (6)

• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• A spin foam model for general Lorentzian 4-geometries
• Asymptotic analysis of spin foam amplitude with timelike triangles

Cited by in corpus (3)

• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Geometry from local flatness in Lorentzian spin foam theories
• Hessian in the spinfoam models with cosmological constant