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- W4313305010 abstract "Dirac's leaping insight that the normalized anti-commutator of the {gamma}^{mu} matrices must equal the timespace signature {eta}^{mu}{nu} was decisive for the success of his equation. The {gamma}^{mu}-s are the same in all Lorentz frames and describe some new degrees of freedom, belonging to some internal motion in the electron. Therefore, the imposed link to {eta}^{mu}{nu} constitutes a separate postulate of Dirac's theory. I derive a manifestly covariant first order equation from the direct quantization of the classical 4-momentum vector using the formalism of Geometric Algebra. All properties of the Dirac electron & positron follow from the equation - preconceived 'internal degrees of freedom', ad hoc imposed signature and matrices unneeded. In the novel scheme, the Dirac operator is frame-free and manifestly Lorentz invariant. Relative to a Lorentz frame, the classical spacetime frame vectors e^{mu} appear instead of the {gamma}^{mu} matrices. Axial frame vectors (without cross product) of the 3D orientation space defining spin and rotations appear instead of the Pauli matrices; polar frame vectors of the 3D position space naturally define boosts, etc. Not the least, the formalism shows a significantly higher computational efficiency compared to matrices." @default.
- W4313305010 created "2023-01-06" @default.
- W4313305010 creator A5080776592 @default.
- W4313305010 date "2022-12-27" @default.
- W4313305010 modified "2023-09-27" @default.
- W4313305010 title "The Real Dirac Equation" @default.
- W4313305010 doi "https://doi.org/10.48550/arxiv.2212.13568" @default.
- W4313305010 hasPublicationYear "2022" @default.
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