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

Pietro Dona; Giorgio Sarno

doi:10.1007/s10714-018-2452-7

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

General Relativity and Quantum Cosmology 2018-09-20 v3

Authors: Pietro Dona , Giorgio Sarno

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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.

Cite

@article{arxiv.1807.03066,
  title  = {Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory},
  author = {Pietro Dona and Giorgio Sarno},
  journal= {arXiv preprint arXiv:1807.03066},
  year   = {2018}
}

Comments

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/

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

Abstract

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