How-To compute EPRL spin foam amplitudes

TL;DR

This paper provides a comprehensive, pedagogical guide to computing EPRL spin foam transition amplitudes, including practical implementation details and analysis of approximation schemes, to lower the entry barrier for researchers in quantum gravity.

Contribution

It offers the first detailed, step-by-step tutorial on calculating EPRL-FK amplitudes with numerical methods and discusses new approximation techniques.

Findings

Successful numerical implementation using sl2cfoam-next

Analysis of advantages and disadvantages of the approach

Introduction of a novel approximation scheme

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.