Topological evolution of classical electromagnetic fields and the photon

The theory of classical electromagnetism is constructed in terms of two exterior di®erential systems, F ¡ dA = 0, and J ¡ dG = 0, which act as topological constraints on the variety of independent variables fx; y; z; tg. These two fundamental constraints lead to two other independent concepts of topological torsion, A^F, and topological spin, A^G, which are explicitly dependent upon the po-tentials, A: The exterior derivative of these 3-forms creates the two familiar Poincare deformation invariants of an electromagnetic sys-tem, valid in the vacuum or plasma state. When the Poincare in-variants vanish, the closed integrals of A^F and A^G exhibit topo-logical invariant properties similar to the "quantized " chiral and spin properties of a photon. The possible evolution of these and other topological properties is studied with respect to classes of pro-cesses that can be de¯ned in terms of singly parameterized vector ¯elds. Non-zero values of the Poincare invariants are the source of topological change and non-equilibrium thermodynamics.