2022/10/11 by Sylvain D. Bréchet, Brechet, Sylvain D.
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Topics in Algebra #Algebraic and Geometric Analysis #Classical Physics (physics.class-ph) #FOS: Physical sciences
paper · pdf · doi:10.48550/arxiv.2210.05601
openalex publication_date 2022/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the electrodynamics of electric charges and currents in vacuum and then generalise our results to the description of a dielectric and magnetic material medium : first in spatial algebra (SA) and then in space-time algebra (STA). Introducing a polarisation multivector P = \boldsymbolp - (1)/(c) \boldsymbolM and an auxiliary electromagnetic field multivector G = ε0 F + P, we express the Maxwell equation in the material medium in SA. Introducing a bound current vector J = J - c ∇⋅P in space-time, the Maxwell equation is then expressed in STA. The wave equation in the material medium is obtained by taking the gradient of the Maxwell equation. For a uniform electromagnetic medium consisting of induced electric and magnetic dipoles, the stress-energy momentum vector is written as T(∇) = (1)/(c) J ⋅ F = f where f is the electromagnetic force density vector in space-time. Finally, the Maxwell equation in the material medium can be written in STA as a wave equation for the potential vector A.