Covariant Isotropic Constitutive Relations in Clifford's Geometric Algebra

Abstract

Constitutive relations for isotropic material media are formulated in a manifestly covariant manner. Clifford's geometric algebra is used throughout. Polarisable,chiral and Tellegen medium are investigated. The investigation leads to the discovery of an underlying algebraic structure that completely classifies isotropic media. Variational properties are reviewed,special attention is paid to the imposed constraints on material parameters. Covariant reciprocity condition is given. Finally,duality transformations and their relevance to constitutive relations are investigated. Duality is shown to characterise 'well-behavedness' of medium which has an interesting metric tensor related implication.