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Lorentzian proper vertex amplitude: Asymptotics

Jonathan Engle1,2,*, Ilya Vilensky1,†, and Antonia Zipfel2,3,‡

  • 1Department of Physics, Florida Atlantic University, Boca Raton, Florida 33431, USA
  • 2Department Physik Universität Erlangen, Institut für Quantengravitation, Staudtstrasse 7, D-91058 Erlangen, Germany
  • 3Instytut Fizyki Teoretycznej, Uniwersytet Warszawski, ul. Hoża 69, 00-681 Warsaw, Poland

  • *jonathan.engle@fau.edu
  • †ilya.vilensky@fau.edu
  • ‡antonia.zipfel@fuw.pl
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Phys. Rev. D 94, 064025 – Published 9 September, 2016

DOI: https://doi.org/10.1103/PhysRevD.94.064025

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 semiclassical limit. The starting point of the analysis is an expression for the amplitude as an action integral with action differing from that in the Engle-Pereira-Rovelli-Livine (EPRL) case by an extra “projector” term. This extra term scales linearly with spins only in the asymptotic limit, and is discontinuous on a (lower dimensional) submanifold of the integration domain in the sense that its value at each such point depends on the direction of approach. New tools are introduced to generalize stationary phase methods to this case. For the case of boundary data which can be glued to a nondegenerate 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.

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See Also

Lorentzian proper vertex amplitude: Classical analysis and quantum derivation

Jonathan Engle and Antonia Zipfel
Phys. Rev. D 94, 064024 (2016)

Article Text

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Phys. Rev. D 94, 064025– Published 9 September, 2016
  • Received 31 May 2016
Article part of CHORUS

© 2016 American Physical Society

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