qg-cpt-marseille/sl2cfoam

Library for computing EPRL transition amplitudes in Loop Quantum Gravity.

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

The intricated combinatorial structure and the non-compactness of the 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 vertex amplitude in the intertwiner basis and some utilities to evaluate SU(2) invariants, booster functions and SL(2,C) Clebsch-Gordan coefficients.

Compiling and using

Linux/Unix system supported. Few libraries are needed :

• Wigxjpf (http://fy.chalmers.se/subatom/wigxjpf/) to compute 3j,6j and 9j symbols. This is included in the ext/ directory and must be built before compiling sl2cfoam.

• GMP (https://gmplib.org/) to compute d-small Wigner matrices for coherent states and for booster function.

• MPFR (http://www.mpfr.org). As GMP, high precision library for floating points. Used in coherent states and boosters computations.

• MPC (http://www.multiprecision.org/mpc/). As GMP and MPFR, high precision library for complex numbers. Used for booster functions.

• GSL (https://www.gnu.org/software/gsl/doc/html/intro.html) to compute complex gamma functions in booster functions.

• OpenMp (http://www.openmp.org/) to parallelize the computation.

To build the sl2cfoam library you can type:

• make creates the library and compiles the test programs.
• make test compiles only test programs.
• ./testall launches test programs.

Then, to link the library to your program you can use the flag -lsl2cfoam. Also, you have to include the main header inc/sl2cfoam.h. In test/ there are several test files that you can look at to learn how to use the library.

Licenses

sl2cfoam is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

sl2cfoam is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.