https://github.com/tsgut/matrix-generators-for-su2-and-su3
Computes the generators for a given representation of SU2 and SU3.
https://github.com/tsgut/matrix-generators-for-su2-and-su3
bprobe bprobem fuzzy-spaces lie-algebra lie-groups mathematica mathematica-notebook matrices matrix matrix-geometry matrix-models quantum-geometry representation-theory representations wolfram-mathematica
Last synced: 2 months ago
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Computes the generators for a given representation of SU2 and SU3.
- Host: GitHub
- URL: https://github.com/tsgut/matrix-generators-for-su2-and-su3
- Owner: TSGut
- License: gpl-3.0
- Created: 2018-06-04T07:36:28.000Z (almost 7 years ago)
- Default Branch: main
- Last Pushed: 2021-01-19T21:10:22.000Z (over 4 years ago)
- Last Synced: 2025-01-22T07:49:32.974Z (4 months ago)
- Topics: bprobe, bprobem, fuzzy-spaces, lie-algebra, lie-groups, mathematica, mathematica-notebook, matrices, matrix, matrix-geometry, matrix-models, quantum-geometry, representation-theory, representations, wolfram-mathematica
- Language: Mathematica
- Size: 23.4 KB
- Stars: 2
- Watchers: 2
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
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# Matrix-Generators-for-SU2-and-SU3
Computes the generators for a given representation of SU2 and SU3 as a list of matrices.
`MatrixRepSU2` in SU2Gen.m returns a specific matrix representation of the group SU(2) with dimension as given via non-optional argument. The method returns a [`List`] of three matrices.
`MatrixRepSU3` in SU3Gen.m returns a specific matrix representation of the group SU(3) with [highest weight] as given via non-optional argument, e.g. for `{1,0}` it will return the [Gell-Mann matrices]. The method returns a [`List`] of eight matrices.
These two Wolfram Mathematica notebooks are a part of [BProbeM], an open source Mathematica package to scan matrix geometries, forked from the original [BProbe]. The particular instances presented here have only been minimally modified to work as stand-alone functions instead of being part of a package. I suggest looking at the internal documentation via comments as well as thinking about the scaling your particular application requires.
The notebooks can in principle be added to Mathematica as part of the BProbeM package if desired but I believe they can perhaps be useful for other purposes and presenting them separate from the BProbeM package can help people who are looking for such an implementation to find them more easily.
For the purposes of citing if you use this in projects / research, please see the full [BProbeM] package.
## Software License
The code for these two notebooks is subject to GNU General Public License v3.0, see the original variant [here].
The two notebooks that are part of Matrix-Generators-for-SU2-and-SU3 are free software: you can redistribute them and/or modify
them 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.
This software 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 software. If not, see .
[`List`]: https://reference.wolfram.com/language/ref/List.html
[highest weight]: https://en.wikipedia.org/wiki/Weight_%28representation_theory%29
[Gell-Mann matrices]: https://en.wikipedia.org/wiki/Gell-Mann_matrices
[BProbe]: https://github.com/lschneiderbauer/BProbe
[BProbeM]: https://github.com/TSGut/BProbeM/
[here]: https://github.com/lschneiderbauer/BProbe