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.
Published in Poincare Group, Photon, V. Dvoeglaz editor
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