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Maxwell's equations outside electrodynamics?

  1. Feb 10, 2012 #1
    So I've been reading Hehl's Foundations of Classical Electrodynamics - which builds up Electrodynamics from a six of axioms - and their proof that the conservation of charge alone is sufficient to derive the inhomogenous Maxwell equations got me thinking - why don't these extremrly basic equations show up everywhere?

    The example from the book basically showed that since charge is conserved (in the language of differential forms, dJ = 0, J being the charge/current 3-form), it is expressible (at least locally, via Poincare's theorem, and they go on to show how it holds globally) as the exterior derivative of a 2-form H: e.g. dH = J -- which is the inhomogenous Maxwell equations, as desired.

    So -- from just that, it would appear that *any* conserved quantity Q (eg dQ = 0) should at least lead to the creation of fields that follow those equations, right? I got to thinking of conserved quantities to try to find a counterexample, but I hit a wall...energy/momentum and mass/energy *are* the source of fields (and IIRC they follow dF=8∏T) , and so is color-charge, but that's cheating because it's just a generalization of electrodynamics. But...what else is there?

    So...what am I missing here? The fact that it deals with conserved quantities makes it seem like it could be somehow related to Noether's theorem, but it seems like if conserved quantities always lead to fields, that fact would be more well-known.
  2. jcsd
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