Einstein equation from covariant loop quantum gravity in semiclassical continuum limit

Muxin Han
Phys. Rev. D 96, 024047 – Published 26 July 2017

Abstract

In this paper we explain how four-dimensional general relativity and, in particular, the Einstein equation, emerge from the spin-foam amplitude in loop quantum gravity. We propose a new limit that couples both the semiclassical limit and continuum limit of spin-foam amplitudes. The continuum Einstein equation emerges in this limit. Solutions of the Einstein equation can be approached by dominant configurations in spin-foam amplitudes. A running scale is naturally associated to the sequence of refined triangulations. The continuum limit corresponds to the infrared limit of the running scale. An important ingredient in the derivation is a regularization for the sum over spins, which is necessary for the semiclassical continuum limit. We also explain in this paper the role played by the so-called flatness in spin-foam formulation, and how to take advantage of it.

  • Received 26 May 2017

DOI:https://doi.org/10.1103/PhysRevD.96.024047

© 2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Muxin Han

  • Department of Physics, Florida Atlantic University, 777 Glades Road, Boca Raton, Florida 33431, USA and Institut für Quantengravitation, Universität Erlangen-Nürnberg, Staudtstr. 7/B2, 91058 Erlangen, Germany

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Issue

Vol. 96, Iss. 2 — 15 July 2017

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