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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.
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J. W. Barrett, R. J. Dowdall, W. J. Fairbairn, F. Hellmann, and R. Pereira, ’’Lorentzian spin foam amplitudes: Graphical calculus and asymptotics,‘‘ Class. Quant. Grav
2010
Cited alongside, same era.
J. W. Barrett, R. J. Dowdall, W. J. Fairbairn, H. Gomes, F. Hellmann, and R. Pereira, ’’Asymptotics of 4d spin foam models,‘‘ Gen. Rel. Grav
2011
Cited alongside, same era.
W. Kaminski, M. Kisielowski, and H. Sahlmann, ’’Asymptotic analysis of the EPRL model with timelike tetrahedra,‘‘ Class. Quant. Grav
2018
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H. Liu and M. Han, ’’Asymptotic analysis of spin foam amplitude with timelike triangles,‘‘ Phys. Rev
2019
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