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

TL;DR

This paper introduces exttt{sl2cfoam}, a C library that efficiently computes Lorentzian EPRL spin foam transition amplitudes, addressing computational challenges in quantum gravity models involving the Lorentz group.

Contribution

The paper presents a new computational tool, exttt{sl2cfoam}, for evaluating Lorentzian EPRL vertex amplitudes, improving efficiency and usability in spin foam calculations.

Findings

Efficient computation of Lorentzian EPRL vertex amplitudes.

Implementation of utilities for SU(2) invariants and Clebsch-Gordan coefficients.

Analysis of data storage, parallelization, and performance metrics.

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.