arXiv subjects

Julio César Jaramillo Quiceno

Publications and source records attributed to Julio César Jaramillo Quiceno.

5 recordsLinked to original sources

arXiv2026

An Introduction to the $p$-Differential Forms in Spinor Variables on the Minkowskian Manifold

This article presents an introductory study of $p$-differential forms in spinor variables defined on the Minkowskian (or Lorentzian) manifold. Starting from the algebraic and geometric foundations of spinor spaces and Clifford algebras, we establish the correspondence between Minkowski spacetime and Hermitian matrices in spinor coordinates. Within this framework, we construct differential 1-forms and 2-forms expressed in spinor notation, and formulate the Dirac operator in terms of exterior calculus. Furthermore, we extend this approach to the case of non-monogenic functions, following the method proposed in~\cite{Jaramillo2024}. The results illustrate the consistency of the spinorial exterior calculus and its potential applications in the study of relativistic field equations and geometric formulations of quantum theory.

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arXiv2026

A Metric-Deformed $q$-Gauge Dirac Equation

We construct a family of metric-deformed gauge theories based on a recently introduced $q$-Dirac operator $D_q = γ^μ\sqrt{|g^{μμ}|}\partial_μ$, which arises from a deformed D'Alembertian $\Box_q = |g^{00}|\partial_t^2 - \sum_i |g^{ii}|\partial_i^2$. The deformation parameter $q$ is related to the metric components via $q_μ= \sqrt{|g^{μμ}|}$. By promoting $g^{μμ}(x)$ to spacetime-dependent background fields, we define a deformed covariant derivative $D_μ^{(q)} = \partial_μ+ ieA_μ(x)/\sqrt{|g^{μμ}(x)|}$ (no sum over $μ$). The corresponding field strength $F_{μν}^{(q)} = [D_μ^{(q)}, D_ν^{(q)}]$ acquires new terms proportional to $\partial_μ(1/\sqrt{|g^{νν}|})$, which vanish for constant metrics. We write down gauge-invariant actions for deformed Yang-Mills theory and for fermions minimally coupled to $D_μ^{(q)}$. This work provides a mathematical foundation for $q$-deformed gauge theories from a metric perspective.

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arXiv2026

Metric-Deformed Heisenberg Algebras and the $q$-Dirac Operator

We introduce a family of metric-deformed Heisenberg algebras $M_1$ and $M_2$, where the commutation relations are expressed directly in terms of the components of a diagonal Lorentzian metric. We show that these algebras unify several known $q$-deformed Heisenberg algebras, including the $q$-$\hbar$ algebra, the new $q$-Heisenberg algebra, and the $q$-generalized Heisenberg algebra, which embed as special cases. Using Sylvester's theorem of inertia, we establish a connection between the metric signature and the deformation parameters. We construct a $q$-Dirac operator $D_q$ from the deformed D'Alembertian and prove that $D_q^2$ recovers the deformed Klein-Gordon operator. Furthermore, we relate this construction to the quadratic $q$-Dirac operator previously introduced by the author, providing a unified framework that bridges spacetime geometry and $q$-deformed quantum algebras.

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arXiv2025

$q$-Heisenberg Algebra in $\otimes^{2}-$Tensor Space

In this paper, we introduce the $q$-Heisenberg algebra in the tensor product space $\otimes^2$. We establish its algebraic properties and provide applications to the theory of non-monogenic functions. Our results extend known constructions in $q$-deformed algebras and offer new insights into functional analysis in non-commutative settings.

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arXiv2025

$q$-Deformed Heisenberg Picture Equation

In this paper we introduce the $q$-deformed Heisenberg picture equation. We consider some examples such as : the spinless particle, the electrón interaction with a magnnetic field and $q$-deformed harmonnic oscillator. The $q$-Heisenberg picture equation for any dynamical function at the end of the paper.

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