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Left- and Right-Chiral Dirac Spinors In a Unified 4D Spinor Space and Their Vector-Sum Decomposition Into Four-Component Weyl Spinors

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Název: Left- and Right-Chiral Dirac Spinors In a Unified 4D Spinor Space and Their Vector-Sum Decomposition Into Four-Component Weyl Spinors
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 Dirac and Weyl spinors are realized as four-component objects living in a common vector space. Within this extended framework there is enough room for both left- and right-chiral Dirac spinors. These two distinct species transform under the left- and right-handed representations, respectively. Furthermore, each Dirac spinor (left- or-right-chiral) can be expressed as a vector sum -rather than a direct sum- of left- and right-chiral four-component Weyl spinors. Crucially, the Dirac spinor and its components now transform under the same spinor space, permitting an unambiguous identification of chiral constituents. This formalism provides a symmetric and geometrically transparent reinterpretation of Dirac spinors and may offer new insights into extended spinor models and relativistic field theories.
Druh dokumentu: Article
DOI: 10.20944/preprints202508.1233.v1
DOI: 10.5281/zenodo.16881383
DOI: 10.5281/zenodo.16883855
DOI: 10.5281/zenodo.16890790
DOI: 10.5281/zenodo.16881384
DOI: 10.5281/zenodo.16919773
Rights: CC BY
Přístupové číslo: edsair.doi.dedup.....1da872a71c47486d4a5ebdbdff8ac74a
Databáze: OpenAIRE
Popis
Abstrakt:We introduce a novel four-dimensional spinor representation of the Lorentz group in which Dirac and Weyl spinors are realized as four-component objects living in a common vector space. Within this extended framework there is enough room for both left- and right-chiral Dirac spinors. These two distinct species transform under the left- and right-handed representations, respectively. Furthermore, each Dirac spinor (left- or-right-chiral) can be expressed as a vector sum -rather than a direct sum- of left- and right-chiral four-component Weyl spinors. Crucially, the Dirac spinor and its components now transform under the same spinor space, permitting an unambiguous identification of chiral constituents. This formalism provides a symmetric and geometrically transparent reinterpretation of Dirac spinors and may offer new insights into extended spinor models and relativistic field theories.
DOI:10.20944/preprints202508.1233.v1