where d is the exterior derivative, ⋆ ⋆ is the Hodge star, J = − − J x d x − − J y d y − − J z d z + ρ ρ d t (where J → → is the electric current density, and ρ ρ is the electric charge density) is the 4-current density 1-form, is the differential forms version of Maxwell's equations.