An Introduction to the p-Differential Forms in Spinor Variables on the Minkowskian Manifold
Abstract
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.
Related
- McKean-Vlasov Differential Equations: An introduction and a focus on some kinetic models
- Geometric Phase and Spinor Beam Dynamics of Paraxial Beams
- Fixed-spinor radial solutions of a perturbed Euclidean spinorial Yamabe equation
- Pure Spinor Factorization of Belinski-Zakharov Solitons and Regular Gravitational Instantons
- Categorical reconstruction of del Pezzo surfaces: Hochschild--Serre algebras and spinor modifications
BibTeX
@misc{quiceno2026introduction,
title = {{An Introduction to the $p$-Differential Forms in Spinor Variables on the Minkowskian Manifold}},
author = {Julio César Jaramillo Quiceno},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14240},
eprint = {2610.14240},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14240},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Introduction to the p-Differential Forms in Spinor Variables on the Minkowskian Manifold
AU - Julio César Jaramillo Quiceno
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.14240
UR - https://arxiv.org/abs/2610.14240
AB - 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.
ER -