Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics
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2024
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| author | Stoilova, N. I. Van der Jeugt, J. |
| author_facet | Stoilova, N. I. Van der Jeugt, J. |
| contents | A $Z_2\times Z_2$-graded Lie superalgebra $g$ is a $Z_2\times Z_2$-graded algebra with a bracket $[.,.]$ that satisfies certain graded versions of the symmetry and Jacobi identity. In particular, despite the common terminology, $g$ is not a Lie superalgebra. We construct the most general orthosymplectic $Z_2\times Z_2$-graded Lie superalgebra $osp(2m_1+1,2m_2|2n_1,2n_2)$ in terms of defining matrices. A special case of this algebra appeared already in work of Tolstoy in 2014. Our construction is based on the notion of graded supertranspose for a $Z_2\times Z_2$-graded matrix. Since the orthosymplectic Lie superalgebra $osp(2m+1|2n)$ is closely related to the definition of parabosons, parafermions and mixed parastatistics, we investigate here the new parastatistics relations following from $osp(2m_1+1,2m_2|2n_1,2n_2)$. Some special cases are of particular interest, even when one is dealing with parabosons only. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_11952 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics Stoilova, N. I. Van der Jeugt, J. Mathematical Physics High Energy Physics - Theory Group Theory Quantum Physics A $Z_2\times Z_2$-graded Lie superalgebra $g$ is a $Z_2\times Z_2$-graded algebra with a bracket $[.,.]$ that satisfies certain graded versions of the symmetry and Jacobi identity. In particular, despite the common terminology, $g$ is not a Lie superalgebra. We construct the most general orthosymplectic $Z_2\times Z_2$-graded Lie superalgebra $osp(2m_1+1,2m_2|2n_1,2n_2)$ in terms of defining matrices. A special case of this algebra appeared already in work of Tolstoy in 2014. Our construction is based on the notion of graded supertranspose for a $Z_2\times Z_2$-graded matrix. Since the orthosymplectic Lie superalgebra $osp(2m+1|2n)$ is closely related to the definition of parabosons, parafermions and mixed parastatistics, we investigate here the new parastatistics relations following from $osp(2m_1+1,2m_2|2n_1,2n_2)$. Some special cases are of particular interest, even when one is dealing with parabosons only. |
| title | Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics |
| topic | Mathematical Physics High Energy Physics - Theory Group Theory Quantum Physics |
| url | https://arxiv.org/abs/2402.11952 |