How-To compute EPRL spin foam amplitudes

Abstract

Spin foam theory is a concrete framework for quantum gravity where numerical calculations of transition amplitudes are possible. Recently, the field became very active, but the entry barrier is steep, mainly because of its unusual language and notions scattered around the literature. This paper is a pedagogical guide to spin foam transition amplitude calculations. We show how to write an EPRL-FK transition amplitude, from the definition of the 2-complex to its numerical implementation using \texttt{sl2cfoam-next}. We guide the reader using an explicit example balancing mathematical rigor with a practical approach. We discuss the advantages and disadvantages of this approach and provide a novel look at a recently proposed approximation scheme.

28 pages with many colored figures. Paper published in the special issue "Probing the Quantum Space-Time" of Universe. v-2 Added introductory section. Matching published version. [QISS]

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Cited by in corpus (13)

• Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-${\Delta }_3$ complex
• Spin-foams as semi-classical vertices: gluing constraints and a hybrid algorithm
• Markov Chain Monte Carlo methods for graph refinement in Spinfoam Cosmology
• Summing bulk quantum numbers with Monte Carlo in spin foam theories
• Spinfoams and high performance computing
• Radiative corrections to the Lorentzian EPRL spin foam propagator
• Lorentzian quantum cosmology from effective spin foams
• Spinfoams: Foundations
• Numerical approach to the black-to-white hole transition
• Curvature effects in the spectral dimension of spin foams
• Toward matter dynamics in spin foam quantum gravity
• A Monte Carlo algorithm for spin foam intertwiners
• (2+1) Lorentzian quantum cosmology from spin-foams: opportunities and obstacles for semi-classicality