Spacetime Formulation Of Electromagnetism

Let R denote the position in spacetime, V the derivative of R with respect to the proper time, P the product of mass and V, and, J the product of charge density and V. The net spacetime force is the derivative of P with respect to the proper time. If F denotes the electromagnetic tensor, and G a variant, Maxwell's equations can be written as ∇ F = μ₀ J and ∇ G = 0. Also, the spacetime electromagnetic force on a point mass of charge q is q F V.