Quantum Superspace and Bloch Electron Systems with Zeeman Effects: *-Bracket Formalism for Super Curtright-Zachos Algebras
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912715682873344 |
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| author | Sato, Haru-Tada |
| author_facet | Sato, Haru-Tada |
| contents | We introduce supersymmetric extensions of the Hom-Lie deformation of the Virasoro algebra (super Curtright-Zachos algebra), as realized in the GL(1,1) quantum superspace, for Bloch electron systems under Zeeman effects. By examining the duality inherent in quantum superspace scaling operators, we establish a correspondence between quantum superspace and its physical realization through a novel operator mixing mechanism. For the continuous case, we construct super Curtright-Zachos algebra using magnetic translations and spin matrix bases, demonstrating explicit realizations for both N=1 and N=2 supersymmetric algebras with a natural N=2 decomposition. For the discrete case, we establish cyclic matrix representations in tight-binding models. We organize these structures through the *-bracket formalism with Z2-grading, revealing how the quantum superspace structure manifests in physical systems while preserving essential algebraic properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17030 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Superspace and Bloch Electron Systems with Zeeman Effects: *-Bracket Formalism for Super Curtright-Zachos Algebras Sato, Haru-Tada High Energy Physics - Theory Mathematical Physics 17B61, 17B68, 81R50, 81R60 We introduce supersymmetric extensions of the Hom-Lie deformation of the Virasoro algebra (super Curtright-Zachos algebra), as realized in the GL(1,1) quantum superspace, for Bloch electron systems under Zeeman effects. By examining the duality inherent in quantum superspace scaling operators, we establish a correspondence between quantum superspace and its physical realization through a novel operator mixing mechanism. For the continuous case, we construct super Curtright-Zachos algebra using magnetic translations and spin matrix bases, demonstrating explicit realizations for both N=1 and N=2 supersymmetric algebras with a natural N=2 decomposition. For the discrete case, we establish cyclic matrix representations in tight-binding models. We organize these structures through the *-bracket formalism with Z2-grading, revealing how the quantum superspace structure manifests in physical systems while preserving essential algebraic properties. |
| title | Quantum Superspace and Bloch Electron Systems with Zeeman Effects: *-Bracket Formalism for Super Curtright-Zachos Algebras |
| topic | High Energy Physics - Theory Mathematical Physics 17B61, 17B68, 81R50, 81R60 |
| url | https://arxiv.org/abs/2412.17030 |