Semiclassical regime of Regge calculus and spin foams

Abstract

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.

arXiv comment30 pages, no figures. Updated version with minor corrections, one reference added

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• On the semiclassical limit of 4d spin foam models
• Space-Time Structure of Loop Quantum Black Hole
• LQG propagator from the new spin foams
• Self-dual Black Holes in LQG: Theory and Phenomenology
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• Spin foam models and the Wheeler-DeWitt equation for the quantum 4-simplex
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• Asymptotics of LQG fusion coefficients
• The new spin foam models and quantum gravity
• Cosine problem in EPRL/FK spinfoam model
• Semi-Classical Holomorphic Transition Amplitudes in Covariant Loop Quantum Gravity
• Causal structure in spin-foams
• A simpler way of imposing simplicity constraints