The Riemann–Silberstein becomes a bivector F = E + I c B = E 1 γ γ 1 γ γ 0 + E 2 γ γ 2 γ γ 0 + E 3 γ γ 3 γ γ 0 − − c ( B 1 γ γ 2 γ γ 3 + B 2 γ γ 3 γ γ 1 + B 3 γ γ 1 γ γ 2 ) , and the charge and current density become a vector J = J μ μ γ γ μ μ = c ρ ρ γ γ 0 + J k γ γ k = γ γ 0 ( c ρ ρ − − J k σ σ k ) .