On the semiclassical limit of 4d spin foam models

By Florian Conrady, L. Freidel. 2008

164 citations recorded by the source corpus.

We study the semiclassical properties of the Riemannian spin foam models with Immirzi parameter that are constructed via coherent states. We show that, in the semiclassical limit, the quantum spin foam amplitudes of an arbitrary triangulation are exponentially suppressed if the face spins do not correspond to a discrete geometry. When they do arise from a geometry, the amplitudes reduce to the exponential of i times the Regge action. Remarkably, the dependence on the Immirzi parameter disappears in this limit.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/34aa7b4b69958449b4479aa8c7103122331f99e0

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Citations in the corpus

The Complete 1/N Expansion of Colored Tensor Models in Arbitrary Dimension (2011, methodology): “The semiclassical limit of various GFT models [30,31] has been analyzed and matter field have been added in the GFT framework [32–34].”
The continuum limit of loop quantum gravity - a framework for solving the theory (2014, background): “Condition (17) is indeed satisfied for spin foams [33], at least for the simplest building blocks that is simplices.”
Twisted geometries: A geometric parametrisation of SU(2) phase space (2010, background): “The motivation for these labels comes from the coherent intertwiners introduced in [8] (for earlier ideas, see also [22]) and further developed in [13], which have proved useful to construct the new EPR-FK-LS spin foam models [9, 10], and crucial to study their semiclassical limit [12, 13, 14] and n”
The Spin-Foam Approach to Quantum Gravity (2012, background): “The authors of [115] write Equation (204) in the following way”
Polyhedra in loop quantum gravity (2010, background): “Specifically, in this limit the transition amplitudes are related to exponentials of the Regge action [9, 31, 56, 57].”
Asymptotic analysis of the EPRL four-simplex amplitude (2009, methodology): “An initial exploration of the asymptotics of the FK model for manifolds without boundary was undertaken in [16].”
Lorentzian spin foam amplitudes: graphical calculus and asymptotics (2009, methodology): “This was considered for the three-dimensional Ponzano–Regge model in [43] and for the Euclidean signature four-dimensional models in [24].”
Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude (2009, methodology): “An initial exploration of the asymptotics of the FK model for manifolds without boundary was undertaken in [16].”