Semiclassical regime of Regge calculus and spin foams

Details Semiclassical regime of Regge calculus and spin foams Semiclassical regime of Regge calculus and spin foams

2008-08-07

arxiv.org/abs/0808.1107v2

Nucl.Phys.B808:546-568,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

30 pages, no figures. Updated version with minor corrections, one reference added

Scientific paper

10.1016/j.nuclphysb.2008.09.005

Recent attempts to recover the graviton propagator from spin foam models involve the use of a boundary quantum state peaked on a classical geometry. The question arises whether beyond the case of a single simplex this suffices for peaking the interior geometry in a semiclassical configuration. In this paper we explore this issue in the context of quantum Regge calculus with a general triangulation. Via a stationary phase approximation, we show that the boundary state succeeds in peaking the interior in the appropriate configuration, and that boundary correlations can be computed order by order in an asymptotic expansion. Further, we show that if we replace at each simplex the exponential of the Regge action by its cosine -- as expected from the semiclassical limit of spin foam models -- then the contribution from the sign-reversed terms is suppressed in the semiclassical regime and the results match those of conventional Regge calculus.

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