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

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.