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arXiv · 2504.07735

$q$-Differential Operators for $q$-Spinor Variables

Julio Cesar Jaramillo Quiceno
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Abstract

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.

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Julio Cesar Jaramillo Quiceno. 2025-04-10. $q$-Differential Operators for $q$-Spinor Variables. https://arxiv.org/abs/2504.07735

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