Asymptotic analysis of spin foam amplitude with timelike triangles

Abstract

The large $j$ asymptotic behavior of $4$-dimensional spin foam amplitude is investigated for the extended spin foam model (Conrady-Hnybida extension) on a simplicial complex. We study the most general situation in which timelike tetrahedra with timelike triangles are taken into account. The large $j$ asymptotic behavior is determined by critical configurations of the amplitude. We identify the critical configurations that correspond to the Lorentzian simplicial geometries with timelike tetrahedra and triangles. Their contributions to the amplitude are phases asymptotically, whose exponents equal to Regge action of gravity. The amplitude may also contains critical configurations corresponding to non-degenerate split signature $4$-simplices and degenerate vector geometries. But for vertex amplitudes containing at least one timelike tetrahedron and one spacelike tetrahedron, critical configurations only give Lorentzian $4$-simplices, while the split signature and degenerate $4$-simplices do not appear.

24+28 pages, 2 figures

References in corpus (7)

• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• A spin foam model for general Lorentzian 4-geometries
• Spin foams with timelike surfaces
• Unitary irreducible representations of SL(2,C) in discrete and continuous SU(1,1) bases
• Timelike twisted geometries

Cited by in corpus (24)

• Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
• 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
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• The Complete Barrett-Crane Model and its Causal Structure
• Analytic Continuation of Spin foam Models
• Asymptotic analysis of spin-foams with time-like faces in a new parameterisation
• 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
• Spikes and spines in 4D Lorentzian simplicial quantum gravity
• Scalar Cosmological Perturbations from Quantum Entanglement within Lorentzian Quantum Gravity
• Finiteness of spinfoam vertex amplitude with timelike polyhedra, and the full amplitude
• Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
• Cosmology in Lorentzian Regge calculus: causality violations, massless scalar field and discrete dynamics
• Curvature effects in the spectral dimension of spin foams
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
• A Monte Carlo algorithm for spin foam intertwiners
• The hessian in spin foam models
• Partial absence of cosine problem in 3d Lorentzian spin foams
• (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality
• A saddle-point finder and its application to the spin foam model