WallGoMatrix is a Mathematica package for computing 2-to-2 scattering matrix elements for arbitrary quantum field theories. It is part of the WallGo project for computing the bubble wall speed for cosmological phase transitions.
WallGo is an open source code for the computation of the bubble wall velocity and bubble wall width in first-order cosmological phase transitions. There is a main Python package together with two subsidiary software packages. The physical and mathematical details are explained in the associated paper.
- WallGo is the name of the main Python package. This determines the wall velocity and width by solving the scalar field(s) equation of motion, the Boltzmann equations and energy-momentum conservation for the fluid velocity and temperature.
- WallGoMatrix computes the relevant matrix elements for the out-of-equilibrium particles, and is written in Mathematica. It builds on existing Mathematica packages DRalgo and GroupMath.
- WallGoCollision performs the higher-dimensional integrals to obtain the collision terms in the Boltzmann equations, and is written in C++. It also has Python bindings so that it can be called directly from Python, but still benefits from the speedup from compiled C++ code.
Users can implement their own models. For WallGoMatrix, the model building routines are taken from DRalgo and involve constructing coupling tensors. The WallGoMatrix routines then contract these coupling tensors with the appropriate kinematic factors to yield the 2-to-2 scattering matrix elements.
WallGoMatrix can be installed as a Wolfram Paclet by running either of the following two commands in Mathematica
PacletInstall["WallGo/WallGoMatrix"];PacletInstall["https://github.com/Wall-Go/WallGoMatrix/releases/latest/download/WallGoMatrix.paclet"];Note that the dependencies of WallGoMatrix must also be installed, for which see the Requirements section below.
WallGoMatrix can alternatively be installed manually by downloading the zip file from the following link:
After unpacking the zip file, place the WallGoMatrix directory inside the Applications folder within either the base or user-specific Mathematica Applications directory. These directories store Mathematica packages and can be located by evaluating the variables $BaseDirectory and $UserBaseDirectory within a Mathematica session.
To find these directories, you can run the following command in Mathematica:
Print["Base Directory: ", FileNameJoin[{$BaseDirectory, "Applications"}]]
Print["User Base Directory: ", FileNameJoin[{$UserBaseDirectory, "Applications"}]]For versions of Mathematica before 14.1, the paths are commonly the following ones
Linux
- /usr/share/Mathematica/Applications
- ~/.Mathematica/Applications
macOS
- ~/Library/Mathematica/Applications
Windows
- C:\ProgramData\Mathematica\Applications
- C:\Users(computer name)\AppData\Roaming\Mathematica\Applications
Note that from Mathematica 14.1 onwards,
these directories are renamed to contain Wolfram instead of Mathematica.
For example, the path for macOS becomes ~/Library/Wolfram/Applications.
WallGoMatrix is written in the Wolfram Mathematica language, and depends on the Mathematica package GroupMath. It has been tested on the following versions.
- Mathematica versions 12.x, 13.x and 14.x
- GroupMath version 1.1.2
GroupMath can be either manually obtained from the link above or by setting the following flag before loading WallGoMatrix in Mathematica
WallGo`WallGoMatrix`$InstallGroupMath=True;WallGoMatrix builds on DRalgo version 1.2, but the required elements are included directly in the WallGoMatrix package, so separate installation of DRalgo is not necessary.
Once the WallGoMatrix directory has been installed, the package can be loaded from within Mathematica using
<<WallGo`WallGoMatrix`To see how WallGoMatrix is used in practice, we recommend taking a look at the examples.
Within WallGo, WallGoMatrix can be executed using Wolframscript. Wolframscript provides the core computational capabilities of Wolfram Mathematica and allows Wolfram Language scripts to be run without needing a full Mathematica installation. To run the example files, you can use the following command:
$ wolframscript -file examples/qcd.m
One requirement for the above command is an active WolframKernel.
Copyright (c) 2024 Andreas Ekstedt, Oliver Gould, Joonas Hirvonen, Benoit Laurent, Lauri Niemi, Philipp Schicho, and Jorinde van de Vis.
This program 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.
This program 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/.