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.

Published in Poincare Group, Photon, V. Dvoeglaz editor
Also presented at the 4th international workshop on Electric and Magnetic Fields, Marseille
May (1998) p.325 A.I. M. Univer. of Liege


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