The source of the field F is the electromagnetic four-current : j = ρ ρ + j , where the scalar part equals the electric charge density ρ, and the vector part the electric current density j. Introducing the electromagnetic potential paravector defined as: A = ϕ ϕ + A , in which the scalar part equals the electric potential ϕ, and the vector part the magnetic potential A. The electromagnetic field is then also: F = ∂ ∂ A ¯ ¯ . The field can be split into electric E = ⟨ ⟨ ∂ ∂ A ¯ ¯ ⟩ ⟩ V and magnetic B = i ⟨ ⟨ ∂ ∂ A ¯ ¯ ⟩ ⟩ B V components. Here, ∂ ∂ = ∂ ∂ t + e 1 ∂ ∂ x + e 2 ∂ ∂ y + e 3 ∂ ∂ z and F is invariant under a gauge transformation of the form A → → A + ∂ ∂ χ χ , where χ χ is a scalar field.