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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.14139 |
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| _version_ | 1866912151581491200 |
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| author | Miranda, Luiza de Freitas, Isaque P. Toppan, Francesco |
| author_facet | Miranda, Luiza de Freitas, Isaque P. Toppan, Francesco |
| contents | The first-order Lévy-Leblond differential equations (LLEs) are the non-relativistic analogous of the Dirac equation: they are the "square roots" of the Schrödinger equation in ($1+d$) dimensions and admit spinor solutions. In this paper we show how to extend to the Lévy-Leblond spinors the real/complex/quaternionic classification of the relativistic spinors (which leads to the notions of Dirac, Weyl, Majorana, Majorana-Weyl, Quaternionic spinors). Besides the free equations, we also consider the presence of potential terms. Applied to a conformal potential, the simplest $(1+1)$-dimensional LLE induces a new differential realization of the $osp(1|2)$ superalgebra in terms of differential operators depending on the time and space coordinates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Classification of the Lévy-Leblond Spinors Miranda, Luiza de Freitas, Isaque P. Toppan, Francesco Mathematical Physics High Energy Physics - Theory Quantum Physics The first-order Lévy-Leblond differential equations (LLEs) are the non-relativistic analogous of the Dirac equation: they are the "square roots" of the Schrödinger equation in ($1+d$) dimensions and admit spinor solutions. In this paper we show how to extend to the Lévy-Leblond spinors the real/complex/quaternionic classification of the relativistic spinors (which leads to the notions of Dirac, Weyl, Majorana, Majorana-Weyl, Quaternionic spinors). Besides the free equations, we also consider the presence of potential terms. Applied to a conformal potential, the simplest $(1+1)$-dimensional LLE induces a new differential realization of the $osp(1|2)$ superalgebra in terms of differential operators depending on the time and space coordinates. |
| title | On the Classification of the Lévy-Leblond Spinors |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2411.14139 |