Generalized Spinfoams

Abstract

We reconsider the spinfoam dynamics that has been recently introduced, in the generalized Kaminski-Kisielowski-Lewandowski (KKL) version where the foam is not dual to a triangulation. We study the Euclidean as well as the Lorentzian case. We show that this theory can still be obtained as a constrained BF theory satisfying the simplicity constraint, now discretized on a general oriented 2-cell complex. This constraint implies that boundary states admit a (quantum) geometrical interpretation in terms of polyhedra, generalizing the tetrahedral geometry of the simplicial case. We also point out that the general solution to this constraint (imposed weakly) depends on a quantum number r_f in addition to those of loop quantum gravity. We compute the vertex amplitude and recover the KKL amplitude in the Euclidean theory when r_f=0. We comment on the eventual physical relevance of r_f, and the formal way to eliminate it.

16 pages, 3 figures

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• Loop quantum gravity: the first twenty five years
• SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
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• Cosmological Constant in LQG Vertex Amplitude
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• Asymptotics of lowest unitary SL(2,C) invariants on graphs
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• Twistorial phase space for complex Ashtekar variables
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• Infrared divergences in the EPRL-FK Spin Foam model
• A note on the secondary simplicity constraints in loop quantum gravity
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• Feynman diagrammatic approach to spin foams
• Numerical analysis of the self-energy in covariant Loop Quantum Gravity
• The Construction of Spin Foam Vertex Amplitudes
• One vertex spin-foams with the Dipole Cosmology boundary
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• Area Propagator and Boosted Spin Networks in Loop Quantum Gravity
• The new spin foam models and quantum gravity
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• Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
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• Geometry from local flatness in Lorentzian spin foam theories
• The kinematical Hilbert space of Loop Quantum Gravity from BF theories
• Commuting Simplicity and Closure Constraints for 4D Spin Foam Models
• Asymptotic of Lorentzian Polyhedra Propagator
• Revisiting EPRL: All Finite-Dimensional Solutions by Naimark's Fundamental Theorem