For the electromagnetic fields (E,B), I propose to use the quaternionic numbers i,j,k:
E=Ew+iEx+jEy+kEz
B=Bw+iBx+jBy+kBz
q=w+ix+jy+kz
∂∂q=∂∂w−i∂∂x−j∂∂y−k∂∂z
∂∂ˉq=∂∂w+i∂∂x+j∂∂y+k∂∂z
The quaternionic Maxwell equations are:
∂E∂t=∂B∂q
div(E)=0
∂B∂t=−∂E∂ˉq
div(B)=0
Can we recover the classical Maxwell equations?