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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2025
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| _version_ | 1866902178074984448 |
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| author | KUNTMAN, M. A. |
| author_facet | KUNTMAN, M. A. |
| contents | <p>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 and their duals. These four distinct species transform under the left- and right-handed and corresponding dual (conjugate) representations, respectively. Furthermore, each Dirac spinor (left, right or dual-right, dual-left) can be expressed as a vector sum -rather than a direct sum- of left- and right-chiral four-component Weyl spinors and their duals. Crucially, Dirac spinors and their 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. </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16919773 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | Left- and Right-Chiral Dirac Spinors In a Unified 4D Spinor Space and Their Vector-Sum Decomposition Into Four-Component Weyl Spinors KUNTMAN, M. A. Dirac spinors 4-component Weyl spinors Extension of the Lorentz algebra Left- and Right-Chiral Dirac Spinors Lie Algebras Decomposition of a Dirac spinor Clifford algebra of spacetime Spinor spaces 4D spinor representations of the Lorentz group <p>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 and their duals. These four distinct species transform under the left- and right-handed and corresponding dual (conjugate) representations, respectively. Furthermore, each Dirac spinor (left, right or dual-right, dual-left) can be expressed as a vector sum -rather than a direct sum- of left- and right-chiral four-component Weyl spinors and their duals. Crucially, Dirac spinors and their 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. </p> |
| title | Left- and Right-Chiral Dirac Spinors In a Unified 4D Spinor Space and Their Vector-Sum Decomposition Into Four-Component Weyl Spinors |
| topic | Dirac spinors 4-component Weyl spinors Extension of the Lorentz algebra Left- and Right-Chiral Dirac Spinors Lie Algebras Decomposition of a Dirac spinor Clifford algebra of spacetime Spinor spaces 4D spinor representations of the Lorentz group |
| url | https://doi.org/10.5281/zenodo.16919773 |