Einstein equation from covariant loop quantum gravity in semiclassical continuum limit
Abstract
In this paper we explain how fourdimensional general relativity and, in particular, the Einstein equation, emerge from the spinfoam amplitude in loop quantum gravity. We propose a new limit that couples both the semiclassical limit and continuum limit of spinfoam amplitudes. The continuum Einstein equation emerges in this limit. Solutions of the Einstein equation can be approached by dominant configurations in spinfoam 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 socalled flatness in spinfoam formulation, and how to take advantage of it.
 Publication:

Physical Review D
 Pub Date:
 July 2017
 DOI:
 10.1103/PhysRevD.96.024047
 arXiv:
 arXiv:1705.09030
 Bibcode:
 2017PhRvD..96b4047H
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 12+3 pages, no figure, presentation improved