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Unified 4D Spinor Space for Dirac and Weyl Spinors: A Vector-Sum Decomposition of the Dirac Spinor

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Název: Unified 4D Spinor Space for Dirac and Weyl Spinors: A Vector-Sum Decomposition of the Dirac Spinor
Autoři: KUNTMAN, M. A.
Publication Status: Preprint
Informace o vydavateli: MDPI AG, 2025.
Rok vydání: 2025
Témata: Clifford algebra of spacetime, Dirac spinors, 4-component Weyl spinors, Extension of the Lorentz algebra, Spinor spaces, Left- and Right-Chiral Dirac Spinors, 4D spinor representations of the Lorentz group, Decomposition of a Dirac spinor, Lie Algebras
Popis: We introduce a novel four-dimensional spinor representation of the Lorentz group in which both Dirac and Weyl spinors are realized as four-component objects living in a common vector space. Furthermore, Dirac spinors can be expressed as vector sum -rather than a direct sum- of left- and right-chiral four-component Weyl spinors. In this representation, Dirac spinors and their left and right components transform under the same spinor space, permitting an unambiguous identification of their chiral constituents. This formalism provides a symmetric and geometrically transparent reinterpretation of Weyl and Dirac spinors and may offer new insights into extended spinor models and relativistic field theories.
Druh dokumentu: Article
DOI: 10.20944/preprints202508.1233.v2
DOI: 10.13140/rg.2.2.32621.29920
DOI: 10.5281/zenodo.17078132
Rights: CC BY
Přístupové číslo: edsair.doi.dedup.....4f98ec1c8c948a9c77fb77a4bec07530
Databáze: OpenAIRE
Popis
Abstrakt:We introduce a novel four-dimensional spinor representation of the Lorentz group in which both Dirac and Weyl spinors are realized as four-component objects living in a common vector space. Furthermore, Dirac spinors can be expressed as vector sum -rather than a direct sum- of left- and right-chiral four-component Weyl spinors. In this representation, Dirac spinors and their left and right components transform under the same spinor space, permitting an unambiguous identification of their chiral constituents. This formalism provides a symmetric and geometrically transparent reinterpretation of Weyl and Dirac spinors and may offer new insights into extended spinor models and relativistic field theories.
DOI:10.20944/preprints202508.1233.v2