  A new formulation of electromagnetism based on linear differential commutator
brackets is developed. Maxwell equations are derived, using these commutator
brackets, from the vector potential $\vec{A}$, the scalar potential $\phi$ and
the Lorentz gauge connecting them. With the same formalism, the continuity
equation is written in terms of these new differential commutator brackets.
  Keywords: Mathematical formulation, Maxwell's equations
