TITLE:
One-to-One Map of Dirac Equation between Matrix Algebra and Geometric Algebra Cl3,0
AUTHORS:
Jesús Sánchez
KEYWORDS:
Geometric Algebra, Matrix Algebra, Dirac Equation, Quantum Mechanics, Wavefunction, Basis Vectors
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.9,
September
18,
2025
ABSTRACT: In this paper, it is created a one-to-one map between the Dirac Equation in Matrix Algebra and the Dirac Equation in Geometric Algebra Cl3,0. The eight free parameters of the spinors in matrix representation correspond to the coefficients of the eight elements of the Geometric Algebra Cl3,0 (scalars, three vectors, three bivectors and the trivector). This way, a one-to-one mapping between matrix representation and Geometric Algebra Cl3,0 can be obtained.