Commutative (Segre’s) Quaternion Fields and Relation with Maxwell Equations

Abstract.

The decomposability of Segre’s quaternion into two complex algebras allows us to introduce, from a mathematical point of view, a four dimensional field by extending the consolidated physical application of complex analysis. The field so introduced is studied in the frame of theory of partial differential systems and its physical features are investigated. This approach can be straightforwardly extended for studying other commutative number systems with an even number of unities.

The quaternion field represents waves and can be associated with a four-potential. These properties stimulate an insight into its relations with Maxwell’s equations. We shall see that some properties are in common with the electromagnetic field and some novelties, which can be considered as starting points for new research fields, grow out of this description.