Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory

  • Pietro DonàEmail author
  • Giorgio Sarno
Research Article


The intricated combinatorial structure and the non-compactness of the Lorentz group have always made the computation of \(SL(2,\mathbb {C})\) EPRL spin foam transition amplitudes a very hard and resource demanding task. With sl2cfoam we provide a C-coded library for the evaluation of the Lorentzian EPRL vertex amplitude. We provide a tool to compute the Lorentzian EPRL 4-simplex vertex amplitude in the intertwiner basis and some utilities to evaluate SU(2) invariants, booster functions and \(SL(2,\mathbb {C})\) Clebsch–Gordan coefficients. We discuss the data storage, parallelizations, time, and memory performances and possible future developments.


Code Loop quantum gravity Spinfoam Vertex amplitude Numerical HPC 



This work was supported in part by the NSF grants PHY-1505411, PHY-1806356 and the Eberly research funds of Penn State. We want to thank François Collet and Francesco Gozzini for providing a basic code for the booster function and the complex gamma function with arbitrary precision floating points numbers and especially for many interesting and helpful discussions. Thanks to NORDITA and to the organizers of the workshop “Quantum Gravity on the Computer”, a very inspiring and useful week in Stockholm. Many thanks to Simone Speziale for fruitful discussions and encouragement and we are very happy to welcome Emilio in this puzzling world.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Physics Department, Institute for Gravitation and the CosmosPenn StateUniversity ParkUSA
  2. 2.Aix Marseille Univ, Université de Toulon, CNRS, CPTMarseilleFrance

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