The Lorentzian proper vertex amplitude: Asymptotics

Abstract

In previous work, the Lorentzian proper vertex amplitude for a spin-foam model of quantum gravity was derived. In the present work, the asymptotics of this amplitude are studied in the semi-classical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the EPRL case by an extra `projector' term which scales linearly with spins only in the asymptotic limit, and is discontinuous on a submanifold of the integration domain. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a non-degenerate Lorentzian 4-simplex, the asymptotic limit of the amplitude is shown to equal the single Feynman term, showing that the extra term in the asymptotics of the EPRL amplitude has been eliminated.

32 pages; argument in section IV clarified and improved

References in corpus (7)

• LQG vertex with finite Immirzi parameter
• A New Spin Foam Model for 4d Gravity
• The loop-quantum-gravity vertex-amplitude
• Flipped spinfoam vertex and loop gravity
• Regularization and finiteness of the Lorentzian LQG vertices
• Divergences and Orientation in Spinfoams
• The Lorentzian proper vertex amplitude: Asymptotics

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• Partial absence of cosine problem in 3d Lorentzian spin foams
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