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 $SL(2,\mathbb{C})$ EPRL spin foam transition amplitudes a very hard and resource demanding task. With \texttt{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.

20 pages, many figures. v2. Typos corrected. v3 minor corrections to match published version. The library can be downloaded at http://bitbucket.org/giorgiosarno/sl2cfoam-1.0/