تقرير
Irreducible representations of $\mathbb{Z}_2^2$-graded ${\cal N} =2$ supersymmetry algebra and $\mathbb{Z}_2^2$-graded supermechanics
| العنوان: | Irreducible representations of $\mathbb{Z}_2^2$-graded ${\cal N} =2$ supersymmetry algebra and $\mathbb{Z}_2^2$-graded supermechanics |
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| المؤلفون: | Aizawa, N., Doi, S. |
| المصدر: | J. Math. Phys. 63 (2022) 091704 |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics |
| الوصف: | Irreducible representations (irreps) of $\mathbb{Z}_2^2$-graded supersymmetry algebra of ${\cal N}=2$ are obtained by the method of induced representation and they are used to derive $\mathbb{Z}_2^2$-graded supersymmetric classical actions. The irreps are four dimensional for $ \lambda = 0$ where $ \lambda $ is an eigenvalue of the Casimir element, and eight dimensional for $\lambda \neq 0.$ The eight dimensional irreps reduce to four dimensional ones only when $\lambda$ and an eigenvalue of Hamiltonian satisfy a particular relation. The reduced four dimensional irreps are used to define $\mathbb{Z}_2^2$-graded supersymmetry transformations and two types of classical actions invariant under the transformations are presented. It is shown that one of the Noether charges vanishes if all the variables of specific $\mathbb{Z}_2^2$-degree are auxiliary. Comment: 17 pages, no figures |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1063/5.0100182 |
| URL الوصول: | http://arxiv.org/abs/2205.07263 |
| رقم الأكسشن: | edsarx.2205.07263 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1063/5.0100182 |
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