The homogeneous equations – Faraday's law of induction and Gauss's law for magnetism combine to form ∂ ∂ σ σ F μ μ ν ν + ∂ ∂ μ μ F ν ν σ σ + ∂ ∂ ν ν F σ σ μ μ = 0 , which may be written using Levi-Civita duality as: