Numerical computations of next-to-leading order corrections in spinfoam large-$j$ asymptotics

Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity

This paper focuses on the semiclassical behavior of the spinfoam quantum gravity in 4 dimensions. There has been long-standing confusion, known as the flatness problem, about whether the curved geometry exists in the semiclassical regime of the spinfoam amplitude. The confusion is resolved by the present work. By numerical computations, we explicitly find curved Regge geometries from the large-$j$ Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam amplitudes on triangulations. These curved geometries are with small deficit angles and relate to the complex critical points of the amplitude.…

On the Asymptotics of Quantum Group Spinfoam Model

Recently a quantum group deformation of EPRL spinfoam model was proposed in arXiv:1012.4216 by one of the authors, and in arXiv:1012.4784 by Fairbairn and Meusburger. It is interesting to study the high spin asymptotics of the quantum group spinfoam model, to see if it gives the discrete Einstein gravity with cosmological constant as its semiclassical limit. In this article we propose a new technique, which can simplify the analysis of the high spin asymptotics for quantum group spinfoam vertex amplitude. This technique can generalize the spinfoam asymptotic analysis developed by Barrett, et a…

Divergences and Orientation in Spinfoams

We suggest that large radiative corrections appearing in the spinfoam framework might be tied to the implicit sum over orientations. Specifically, we show that in a suitably simplified context the characteristic "spike" divergence of the Ponzano-Regge model disappears when restricting the theory to just one of the two orientations appearing in the asymptotic limit of the vertex amplitude.

Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator

We compute numerically the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam propagator on a 4-simplex, by adapting the methods of Lefschetz thimble and Markov Chain Monte-Carlo to oscillatory spinfoam integrals. Our method can compute any spinfoam observables at relatively large spins. We obtain the numerical results of the propagators at different spins and demonstrate their consistency with the expected spinfoam semi-classical behavior in the large spin limit. Our results exhibit significant quantum corrections at smaller spins. Our method is reliable and thus can be employed to disco…

On Spinfoam Models in Large Spin Regime

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 and the so called, almost-analytic machinery, in order to find the asymptotic behavior of the contributions from all possible large spin configurations in the spinfoam model. The spins contributing the sum are written as ${J}_f=λ{j}_f$ where $ł$ is a large parameter resulting in an asymptotic expansion via stationary phase approximation. The analysis shows …

Many-nodes/many-links spinfoam: the homogeneous and isotropic case

I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude for regular graphs, with an arbitrary number of links and nodes, and coherent states peaked on a homogeneous and isotropic geometry. This form of the amplitude can be applied for example to a dipole with an arbitrary number of links or to the 4-simplex given by the compete graph on 5 nodes. All the resulting amplitudes have the same support, independently of the graph used, in the large j (large volume) limit. This implies that they all yield the Friedmann equation: I show this in the presence of the cosmological constant. This res…

具有宇宙学常数的自旋泡沫临界点的几何重构

Geometrical Reconstruction of Spinfoam Critical Points with A Cosmological Constant

本文通过建立SL(2,C)平坦联络模空间与常曲率4-单形几何的对应，利用Fock-Goncharov坐标和旋量重构了具有非零宇宙学常数的4维洛伦兹自旋泡沫振幅临界点，为量子引力修正计算及量子宇宙学和黑洞物理应用奠定算法基础。

Pushing Further the Asymptotics of the 6j-symbol

In the context of spinfoam models for quantum gravity, we investigate the asymptotical behavior of the 6j-symbol at next-to-leading order. We compute it analytically and check our results against numerical calculations. The 6j-symbol is the building block of the Ponzano-Regge amplitudes for 3d quantum gravity, and the present analysis is directly relevant to deriving the quantum corrections to gravitational correlations in the spinfoam formalism.

The 6j-symbol: Recursion, Correlations and Asymptotics

We study the asymptotic expansion of the 6j-symbol using the Schulten-Gordon recursion relations. We focus on the particular case of the isosceles tetrahedron and we provide explicit formulas for up to the third order corrections beyond the leading order. Moreover, in the framework of spinfoam models for 3d quantum gravity, we show how these recursion relations can be used to derive Ward-Takahashi-like identities between the expectation values of graviton-like spinfoam correlations.

Numerical analysis of the self-energy in covariant Loop Quantum Gravity

We study numerically the first order radiative corrections to the self-energy, in covariant loop quantum gravity. We employ the recently developed 'sl2cfoam-next' spinfoam amplitudes library, and some original numerical methods. We analyze the scaling of the divergence with the infrared cutoff, for which previous analytical estimates provided widely different lower and upper bounds. Our findings suggest that the divergence is approximately linear in the cutoff. We also investigate the role of the Barbero-Immirzi parameter in the asymptotic behavior, the dependence of the scaling on some bounda…

Sub-leading asymptotic behaviour of area correlations in the Barrett-Crane model

The Barrett-Crane spin foam model for quantum gravity provides an excellent setting for testing analytical and numerical tools used to probe spinfoam models. Here, we complete the report on the numerical analysis of the single 4-simplex area correlations begun in Phys. Lett. B670 (2009) 403-406, discussing the next-to-leading order corrections ("one-loop" corrections) with particular attention to their measure dependence, and the difference between the Gaussian and Bessel ansatze for the boundary state.

Next-to-soft corrections to high energy scattering in QCD and gravity

We examine the Regge (high energy) limit of 4-point scattering in both QCD and gravity, using recently developed techniques to systematically compute all corrections up to next-to-leading power in the exchanged momentum i.e. beyond the eikonal approximation. We consider the situation of two scalar particles of arbitrary mass, thus generalising previous calculations in the literature. In QCD, our calculation describes power-suppressed corrections to the Reggeisation of the gluon. In gravity, we confirm a previous conjecture that next-to-soft corrections correspond to two independent deflection …

次领头后牛顿阶散射双体动力学的辐射反作用修正

Radiation-reaction correction to scattering binary dynamics at the Next-to-Leading Post-Newtonian Order

本文计算了散射双体动力学在次领头后牛顿阶的辐射反作用修正，并在时域和频域中分析了轨道参数修正，为3.5PN精度的辐射损失和波形构建提供了关键输入。