Asymptotic analysis of the EPRL model with timelike tetrahedra

Abstract

We perform the stationary phase analysis of the vertex amplitude for the EPRL spin foam model extended to include timelike tetrahedra. We analyse both, tetrahedra of signature $---$ (standard EPRL), as well as of signature $+--$ (Hnybida-Conrady extension), in a unified fashion. However, we assume all faces to be of signature $--$. The stationary points of the extended model are described again by $4$-simplices and the phase of the amplitude is equal to the Regge action. Interestingly, in addition to the Lorentzian and Euclidean sectors there appear also split signature $4$-simplices.

v2: 97 pages, 4 figures, as published in CQG

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Cited by in corpus (27)

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• Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• Asymptotic analysis of spin foam amplitude with timelike triangles
• Emergent 4-dimensional linearized gravity from spin foam model
• Asymptotic analysis of spin-foams with time-like faces in a new parameterisation
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• Spin-foams as semi-classical vertices: gluing constraints and a hybrid algorithm
• Spinfoams and high performance computing
• Asymptotics of $\mathrm{SL}(2,\mathbb{C})$ coherent invariant tensors
• Numerical evaluation of spin foam amplitudes beyond simplices
• Spinfoams: Foundations
• Finiteness of spinfoam vertex amplitude with timelike polyhedra, and the full amplitude
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• Spikes and spines in 4D Lorentzian simplicial quantum gravity
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• Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics
• Curvature effects in the spectral dimension of spin foams
• A Monte Carlo algorithm for spin foam intertwiners
• The hessian in spin foam models
• Partial absence of cosine problem in 3d Lorentzian spin foams
• A saddle-point finder and its application to the spin foam model
• (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality