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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Main Author: KUNTMAN, M. A.
Format: Recurso digital
Published: Zenodo 2025
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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>
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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