The Ubiquitous Maxwell-Faraday-Ampere

It is remarkable that for any ordered set of variables {t,x,y,z,....}, the 1-form of Action, A = At * dt + Ax*dx + ..., will generate a 2-form F, and if the functions are C2, then dF = 0, for any dimension N. No matter how large N is, the first four equations of dF= 0 are exactly of the same format as the Maxwell - Faraday equations of electro-magnetic theory. No new variables beyond the E and B six components appear in the first 4 equations of dF = 0.

The Maxwell - Faraday equations form a nested set. The fifth and sequentially other equations of dF = 0 do link the higher dimensional components to those classically recognized as the electromagnetic E and B fields. However, no new terms appear in the first four equations!

This result is strong evidence for the topological basis of electromagnetic theory.


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Last update 01/23/2009
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