Free electromagnetic fields on a compact Lie group manifold

Maxwell’s equations for free fields are studied on the underlying C^∞ manifold of a compact Lie group. The formulation is in terms of exterior differential forms as given by Wheeler. It is found that on a compact connected Lie group there are no free electromagnetic fields. The results obtained are essentially a physical interpretation of the well‐known theorem that the second Betti number of a compact semisimple Lie group is zero.