Topological Evolution of Classical Electromagnetic Fields and the Photon

The theory of classical electromagnetism is constructed in terms of two exterior differential systems, F − dA = 0, and J − dG = 0, which act as topological constraints on the variety of independent variables {x, y, z, t}. 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 potentials, A. The exterior derivative of these 3-forms creates the two familiar Poincare deformation invariants of an electromagnetic system, valid in the vacuum or plasma state. When the Poincare invariants vanish, the closed integrals of A^F and A^G exhibit topological 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 processes that can be defined in terms of singly parameterized vector fields. Non-zero values of the Poincare invariants are the source of topological change and non-equilibrium thermodynamics.