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

Abstract

We numerically study the next-to-leading order corrections of the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) 4-simplex amplitude in the large-$j$ expansions. We perform large-$j$ expansions of Lorentzian EPRL 4-simplex amplitudes with two different types of boundary states, the coherent intertwiners and the coherent spin-network, and numerically compute the leading-order and the next-to-leading order $O(1/j)$ contributions of these amplitudes. We also study the dependences of these $O(1/j)$ corrections on the Barbero-Immirzi parameter $\gamma$. We show that they, as functions of $\gamma$, stabilize to finite real constants as $\gamma \to \infty$. Lastly, we obtain the quantum corrections to the Regge action because of the $O(1/j)$ contribution to the spinfoam amplitude.

arXiv comment24 pages, 5 figures

References in corpus (28)

• Background Independent Quantum Gravity: A Status Report
• The Spin Foam Approach to Quantum Gravity
• LQG vertex with finite Immirzi parameter
• A new spinfoam vertex for quantum gravity
• A New Spin Foam Model for 4d Gravity
• Analytic Continuation Of Chern-Simons Theory
• Fundamental Structure of Loop Quantum Gravity
• Lorentzian spin foam amplitudes: graphical calculus and asymptotics
• Asymptotic analysis of the EPRL four-simplex amplitude
• On the semiclassical limit of 4d spin foam models
• Graviton propagator from background-independent quantum gravity
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• LQG propagator from the new spin foams
• Numerical evidence for a phase transition in 4d spin foam quantum gravity
• Coherent spin-networks
• Lorentzian spinfoam propagator
• Path integral representation of spin foam models of 4d gravity
• Numerical study of the Lorentzian Engle-Pereira-Rovelli-Livine spin foam amplitude
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
• Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
• Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory
• Renormalization of symmetry restricted spin foam models with curvature in the asymptotic regime
• Spinfoams in the holomorphic representation
• Path Integral Representation of Lorentzian Spinfoam Model, Asymptotics, and Simplicial Geometries
• Numerical analysis of spin foam dynamics and the flatness problem
• Simple model for quantum general relativity from loop quantum gravity
• Towards the graviton from spinfoams: the complete perturbative expansion of the 3d toy model
• A complex path around the sign problem

Cited by in corpus (12)

• A Short Review of Loop Quantum Gravity
• Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity
• A high-performance code for EPRL spin foam amplitudes
• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Asymptotics of lowest unitary SL(2,C) invariants on graphs
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian
• Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-${\Delta }_3$ complex
• Spinfoams and high performance computing
• Asymptotics of $\mathrm{SL}(2,\mathbb{C})$ coherent invariant tensors
• Spin foam amplitude of the black-to-white hole transition
• A saddle-point finder and its application to the spin foam model
• Hessian in the spinfoam models with cosmological constant