Multiparavector Subspaces of Cℓ_n: Theorems and Applications

Abstract

While Clifford algebras are known to provide appropriate mathematical structures for describing many geometrical relations and physical phenomena, traditional applications use only homogeneous elements (elements of a single grade) to model physical entities such as spacetime vectors in relativity and their transformations. Lower-dimensional realizations of the structures inherent in physical systems are sometimes afforded by exploiting mixed-grade representations of such entities, for example by modeling spacetime vectors by paravectors (sums of scalars and vectors). This contribution explores the geometry of subspaces generated by paravectors of Cℓ_n, the Clifford algebra of n -dimensional Euclidean space, and its applications to physical phenomena.