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

Abstract

The intricated combinatorial structure and the non-compactness of the Lorentz group have always made the computation of SL(2 , 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 , C) Clebsch–Gordan coefficients. We discuss the data storage, parallelizations, time, and memory performances and possible future developments.