$q$-Differential Operators for $q$-Spinor Variables
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913799146045440 |
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| author | Quiceno, Julio Cesar Jaramillo |
| author_facet | Quiceno, Julio Cesar Jaramillo |
| contents | We introduce a \emph{q}-differential operator adapted to \emph{q}-spinor variables, establishing a corresponding \emph{q}-spinor chain rule and defining both standard and Dirac-type \emph{q}-differential operators. Integral formulas in \emph{q}-spinor variables are derived, and applications to \emph{q}-deformed spinor differential equations are explored through explicit examples. The framework extends existing \emph{q}-calculus to spinorial structures, offering potential insights into quantum deformations of relativistic field equations. We conclude with suggestions for future developments, including a \emph{q}-analogue of the Dirac--Maxwell algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $q$-Differential Operators for $q$-Spinor Variables Quiceno, Julio Cesar Jaramillo Mathematical Physics Quantum Physics 81Q99, 46E99, 35A24, 15A66, 16T99 . 17B37 We introduce a \emph{q}-differential operator adapted to \emph{q}-spinor variables, establishing a corresponding \emph{q}-spinor chain rule and defining both standard and Dirac-type \emph{q}-differential operators. Integral formulas in \emph{q}-spinor variables are derived, and applications to \emph{q}-deformed spinor differential equations are explored through explicit examples. The framework extends existing \emph{q}-calculus to spinorial structures, offering potential insights into quantum deformations of relativistic field equations. We conclude with suggestions for future developments, including a \emph{q}-analogue of the Dirac--Maxwell algebra. |
| title | $q$-Differential Operators for $q$-Spinor Variables |
| topic | Mathematical Physics Quantum Physics 81Q99, 46E99, 35A24, 15A66, 16T99 . 17B37 |
| url | https://arxiv.org/abs/2504.07735 |