Lorentzian spin foam amplitudes: graphical calculus and asymptotics
Abstract
The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.
Keywords
Cite
@article{arxiv.0907.2440,
title = {Lorentzian spin foam amplitudes: graphical calculus and asymptotics},
author = {John W. Barrett and Richard J. Dowdall and Winston J. Fairbairn and Frank Hellmann and Roberto Pereira},
journal= {arXiv preprint arXiv:0907.2440},
year = {2014}
}
Comments
30 pages. v2: references now appear. v3: presentation greatly improved (particularly diagrammatic calculus). Definition of "Regge state" now the same as in previous work; signs change in final formula as a result. v4: two references added