Quaternionic formulation of the classical fields

Abstract

In this article we present the quaternionic formulation of classical Maxwell-like field equations using complex quaternions and show that in this formalism they get an elegant, economical and compact form. In the quaternionic description of classical fields two quantities are essential: the field quaternion embracing all field variables and the differential quaternionic operator embracing the time and space differential operators. Applying the quaternionic operator on the field quaternion one gets an equation which contains many individual equations. In this formalism the eight equations of the Maxwell equations can be written as one quaternionic. We describe different types of quaternionic fields and discuss their possible occurrence in nature.