Were Maxwell's equations still condensed to 4 equations (Heaviside's equations in Gibb's vector notation), or something less concise, as I believe they were with quanternions?
Expressing Maxwell's equations using the six-component electromagnetic tensor F, they become
dF = μJ
d*F = 0
where μ is the magnetic permeability of the vacuum and J is the electromagnetic 4-current. The operator 'd' is the differential operator from exterior algebra, and the '*' is the Hodge dual.
Using the bivector field F = E + iB from geometric algebra, they become
DF = μJ
where μ and J are as before, and D is the covector derivative.
For comparison, using the traditional Gibbs/Heaviside notation Maxwell's equations are
∇ . E = ρ/ε
∇ . B = 0
∇ x E = -∂B/∂t
∇ x B = μ(J + ε ∂E/∂t)
