SciPost Submission Page
Irreducible representations of $\mathbb{Z}_2^2$-graded supersymmetry algebra and their applications
by N. Aizawa
Submission summary
| Authors (as registered SciPost users): | Naruhiko Aizawa |
| Submission information | |
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| Preprint Link: | scipost_202211_00040v1 (pdf) |
| Date accepted: | Aug. 11, 2023 |
| Date submitted: | Nov. 23, 2022, 2:32 a.m. |
| Submitted by: | Naruhiko Aizawa |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We give a brief review on recent developments of $\mathbb{Z}_2^n$-graded symmetry in physics in which hidden $\mathbb{Z}_2^n$-graded symmetries and $\mathbb{Z}_2^n$-graded extensions of known systems are discussed. This elucidates physical relevance of the $\mathbb{Z}_2^n$-graded algebras. As an example of physically interesting algebra, we take $\mathbb{Z}_2^2$-graded supersymmetry (SUSY) algebras and consider their irreducible representations (irreps). A list of irreps for ${\cal N} = 1, 2$ algebras is presented and as an application of the irreps, $\mathbb{Z}_2^2$-graded SUSY classical actions are constructed.
Published as SciPost Phys. Proc. 14, 016 (2023)
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2022-12-23 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202211_00040v1, delivered 2022-12-23, doi: 10.21468/SciPost.Report.6378
Strengths
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The paper contains a very nice review of applications of $Z_2^2$ and more generaly $Z_2^n$ graded algebra in physics. In particular the connection with symmetries of Levy-Leblond equation, mixed parabosons and parafermions and clifford algebras. The section 2.2 contain further context in which they have applications.
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The subsection 3.1 present details of the irreducible representations. The results seems correct and are nicely summarized.
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The subsection 3.2 is particularly relevant for this journal as it provide some insight into construction of Z_2^2 graded SUSY classical mechanics.
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The paper is well written and has appropriate references.