DIRECT-PRODUCT AND DECOMPOSITION OF CERTAIN PHYSICALLY IMPORTANT ALGEBRAS

I consider the direct product algebra formed from two isomorphic Cliff ord algebras. More specifically, for an element x in each of the two c omponent algebras I consider. elements in the direct product space wit h the form x x x. I show how this construction can be used to model th e algebraic structure of particular vector spaces with metric, to desc ribe the relationship between wavefunction and observable in examples from quantum mechanics, and to express the relationship between the el ectromagnetic field tensor and the stress-energy tense, in electromagn etism. To enable this analysis I introduce a particular. decomposition of the direct product algebra.