相关论文: Asymptotics of 4d spin foam models

The present paper studies the large-j asymptotics of the Lorentzian EPRL spinfoam amplitude on a 4d simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical…

We fill one of the remaining gaps in the asymptotic analysis of the vertex amplitudes of the Engle-Pereira-Rovelli-Livine (EPRL) spin foam models: We show that the hessian is nondegenerate for the stationary points that corresponds to…

We study the asymptotic geometry of the spin foam partition function for a large class of models, including the models of Barrett and Crane, Engle, Pereira, Rovelli and Livine, and, Freidel and Krasnov. The asymptotics is taken with respect…

Using the coherent state techniques developed for the analysis of the EPRL model we give the asymptotic formula for the Ponzano-Regge model amplitude for non-tardis triangulations of handlebodies in the limit of large boundary spins. The…

The original spin foam model construction for 4D gravity by Barrett and Crane suffers from a few troubling issues. In the simple examples of the vertex amplitude they can be summarized as the existence of contributions to the asymptotics…

We define an effective action for spin foam models of quantum gravity by adapting the background field method from quantum field theory. We show that the Regge action is the leading term in the semi-classical expansion of the spin foam…

Simplicial approaches to quantum gravity such as quantum Regge calculus and spin foams include configurations where bulk edges can become arbitrarily large while the boundary edges are kept small. Spikes and spines are prime examples for…

Numerical methods in spin-foam models have significantly advanced in the last few years, yet challenges remain in efficiently extracting results for amplitudes with many quantum degrees of freedom. In this paper we sketch a proposal for a…

We apply the non-commutative Fourier transform for Lie groups to formulate the non-commutative metric representation of the Ponzano-Regge spin foam model for 3d quantum gravity. The non-commutative representation allows to express the…

We report on the numerical analysis of the area correlations in spin foam gravity on a single 4-simplex considered by Rovelli in PRL 97 (2006) 151301. We compare the asymptotics and confirm the inverse squared distance leading behaviour at…

We numerically estimate the divergence of several two-vertex diagrams that contribute to the radiative corrections for the Lorentzian EPRL spin foam propagator. We compute the amplitudes as functions of a homogeneous cutoff over the bulk…

A certain operator $\T=\int_{\SL}\dd g\, Y^{\dagger}gY$ can be found in various Lorentzian EPRL calculations. The properties of this operator has been studied here in large $j$ limit. The leading order of $\T$ is proportional to the…

We describe a technique to study the asymptotics of SL(2,C) invariant tensors associated to graphs, with unitary irreps and lowest SU(2) spins, and apply it to the Lorentzian EPRL-KKL (Engle, Pereira, Rovelli, Livine; Kaminski, Kieselowski,…

We study the semi-classical limit of the recently proposed coherent spin foam model for (2+1) Lorentzian quantum gravity. Specifically, we analyze the gluing equations derived from the stationary phase approximation of the vertex amplitude.…

The Christensen-Egan algorithm is extended and generalized to efficiently evaluate new spin foam vertex amplitudes proposed by Engle, Pereira & Rovelli and Freidel & Krasnov, with or without (factored) boundary states. A concrete pragmatic…

We propose an explicit spin-foam amplitude for Lorentzian gravity in three dimensions, allowing for both space- and time-like boundaries. The model is based on two main requirements: that it should be structurally similar to its well-known…

We study the 4-d holomorphic Spin Foam amplitude on arbitrary connected 2-complexes and degrees of divergence. With recently developed tools and truncation scheme, we derive a formula for a certain class of graphs, which allows us to write…

We provide an algorithm to estimate the divergence degree of the Lorentzian EPRL-FK spin foam amplitudes for arbitrary 2-complexes. We focus on the "self-energy" and "vertex renormalization" diagrams and find an upper bound estimate. We…

I present some recent progresses in the study of the EPRL self-energy amplitude. New numerical methods allow to analyze how the divergence scales, for which previous works provided very different lower and upper bounds. I show the role that…

We study the semiclassical behavior of Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model, by taking into account the sum over spins in the large spin regime. We also employ the method of stationary phase analysis with parameters…