Four-dimensional Spinfoam Quantum Gravity with Cosmological Constant: Finiteness and Semiclassical Limit

Abstract

We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with cosmological constant. The construction of spinfoam amplitudes uses the state-integral model of PSL(2,$\mathbb{C}$) Chern-Simons theory and the implementation of simplicity constraint. The formulation has 2 key features: (1) spinfoam amplitudes are all finite, and (2) With suitable boundary data, the semiclassical asymptotics of the vertex amplitude has two oscillatory terms, with phase plus or minus the 4-dimensional Lorentzian Regge action with cosmological constant for the constant curvature 4-simplex.

25 pages, 8 figures

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• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• Polyhedra in loop quantum gravity
• Face amplitude of spinfoam quantum gravity
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Cited by in corpus (9)

• Summing bulk quantum numbers with Monte Carlo in spin foam theories
• Lorentzian quantum cosmology from effective spin foams
• Spinfoams: Foundations
• Finiteness of spinfoam vertex amplitude with timelike polyhedra, and the full amplitude
• Curvature effects in the spectral dimension of spin foams
• Toward matter dynamics in spin foam quantum gravity
• Representations of a quantum-deformed Lorentz algebra, Clebsch-Gordan map, and Fenchel-Nielsen representation of complex Chern-Simons theory at level-$N$
• Spinfoam tunneling of quantum geometries in angle variables
• Hessian in the spinfoam models with cosmological constant