TITLE:
The Electromagnetic Field Strength and the Lorentz Force in Geometric Algebra Cl3,0
AUTHORS:
Jesús Sánchez
KEYWORDS:
Geometric Algebra, Covariant Formulation of Classical Electromagnetism, Electromagnetic Field Strength, Lorentz Force, Electromagnetic Trivector
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.6,
June
18,
2025
ABSTRACT: In this paper, it will be calculated the electromagnetic field strength and the Lorentz force in Geometric Algebra Cl3,0. And it will be compared with their equivalent in the tensor covariant formalism. Also, four extra equations not appearing in the classical formalism will be obtained and its meaning will be explained. In the same way, the electromagnetic Field strength elements and the velocity multivector of the particle will be expanded. New equations and new elements appearing will be explained, being the most important one, the Electromagnetic trivector
B
xyz
. A field to be added to the magnetic (bivector-like) and electric (vector-like) fields. Lastly, an insight of the possible implications of these learnings in the Dirac Equation will be commented.