The Topology and Topological Evolution of Electromagnetic Fields and Currents

When it is presumed that classical Electromagnetism can be described in terms of the exterior differential system, F-dA= 0, and J-dG=0, then evolution of the system in the direction of the Torsion vector can be defined. (Recall that the Torsion Vector direction field is unique on spaces of even Pfaff dimension). The topology of the system can be defined in terms of the Pfaff sequence of forms constructed from the elements of the exterior differential system.

Deformation invariant integrals lead to topological properties. For example, the closed integral of the 4 current J is a deformation invariant for ALL evolutionary processes that can be described by a vector field.

Other 3-forms, A^F and A^G and A^W can lead to deformation invariants if the evolutionary processes are restricted. Such restrictions lead to equivalence classes of processes.

It turns out that Topology is not conserved in the direction of the Torsion vector, unless E.B = 0.

In general all symplectic processes are thermodynamically reversible.

A slightly reduced version of the download
classice.pdf has been published in "Photon the Poincare Group", Editor V. Dvoeglazof, Nova Science Publishers, NY 1999, p.246.
The article may be downloaded as photon5.pdf


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Last update 01/23/2009
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