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.
Description
Lorentzian spin foam amplitudes: graphical calculus and asymptotics
%0 Generic
%1 Barrett2009
%A Barrett, John W.
%A Dowdall, Richard J.
%A Fairbairn, Winston J.
%A Hellmann, Frank
%A Pereira, Roberto
%D 2009
%K lorentzian reggecalculus spinfoam
%T Lorentzian spin foam amplitudes: graphical calculus and asymptotics
%U http://arxiv.org/abs/0907.2440
%X 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.
@misc{Barrett2009,
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.
},
added-at = {2009-07-16T11:39:29.000+0200},
author = {Barrett, John W. and Dowdall, Richard J. and Fairbairn, Winston J. and Hellmann, Frank and Pereira, Roberto},
biburl = {https://www.bibsonomy.org/bibtex/2233c5b9a49a229ee6975140bf0f99e7c/random3f},
description = {Lorentzian spin foam amplitudes: graphical calculus and asymptotics},
interhash = {7bf90c9cec4f7581fa3baebfddeb402a},
intrahash = {233c5b9a49a229ee6975140bf0f99e7c},
keywords = {lorentzian reggecalculus spinfoam},
note = {cite arxiv:0907.2440
Comment: 30 pages. v2: references now appear},
timestamp = {2009-07-16T11:39:30.000+0200},
title = {Lorentzian spin foam amplitudes: graphical calculus and asymptotics},
url = {http://arxiv.org/abs/0907.2440},
year = 2009
}