# The Clifford algebra of physical space and Dirac theory

@article{Vaz2016TheCA,
title={The Clifford algebra of physical space and Dirac theory},
author={Jayme Vaz},
journal={European Journal of Physics},
year={2016},
volume={37},
pages={055407}
}
• J. Vaz
• Published 11 July 2016
• Physics
• European Journal of Physics
The claim found in many textbooks that the Dirac equation cannot be written solely in terms of Pauli matrices is shown to not be completely true. It is only true as long as the term in the usual Dirac factorization of the Klein–Gordon equation is assumed to be the product of a square matrix β and a column matrix ψ. In this paper we show that there is another possibility besides this matrix product, in fact a possibility involving a matrix operation, and show that it leads to another possible…
Dirac Theory in Euclidean 3D Geometric Algebra (Cl3)
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• J. Vaz
• Mathematics, Physics
• 2018
Elko spinors are eigenspinors of the charge conjugation operator. In this work we use the Clifford algebra of the physical space in order to formulate the theory of Elko spinors and use a procedure
Operators and Field Equations in the Electroweak Sector of Particle Physics
• G. McClellan
• Physics, Mathematics
• 2021
This paper derives a linear, first-order, partial differential field equation (a Dirac-like equation) in the geometric calculus of the geometric algebra $${\mathcal {G}}_{4,1}$$ that has free
DKP algebra, DKP equation, and differential forms
• Mathematics
Journal of Mathematical Physics
• 2018
It is well known that the Clifford algebras and the Dirac equation have a representation in terms of differential forms known as the Kahler-Atiyah algebra and the Dirac-Kahler equation, respectively.
Spinor Fields, Singular Structures, Charge Conjugation, ELKO and Neutrino Masses
In this paper, we consider the most general treatment of spinor fields, their kinematic classification and the ensuing dynamic polar reduction, for both classes of regular and singular spinors;
On Paravectors and Their Associated Algebras
• J. Vaz
• Mathematics
• 2019
Some algebraic structures that can be defined on the spaces of paravectors and k-paravectors are studied. Firstly, a version of the exterior and interior products resembling those in the exterior
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• 2020
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