Constitutive relations and Clifford algebra in electromagnetism (Q1921265)

The author asserts that the Clifford algebra provides a compact covariant form of electromagnetism and proves that this technique is particularly suitable to discuss constitutive relations and to prove their covariance under a proper Lorentz group. The paper starts with a comprehensive introduction of Clifford algebras relevant to the problem. Next, it discusses the connection between Clifford algebra and electromagnetism in relation to polarization and magnetization. The constitutive relations in linear isotropic (non-aging) media are discussed. It is pointed out that the Maxwell-Clifford equations impose that the components of the electromagnetic field satisfy some integro-differential equation which has to be hyperbolic so that the wave propagates with a finite speed.