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Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I think "inverting" may have been the word the author used.)

The paper was in one of the endorsed groups (not General Physics), and seemed quite authoritative. But I've never seen this property mentioned elsewhere, and wanted to know:

  1. A reference, as stupidly I didn't note the paper's ArXiv code at the time (The reference needn't be to that or another ArXiv paper of course - Quite likely this is better explained in some other source such as a textbook.)

  2. Whether this is considered just a curiosity with no known use or, like the Lorentz transforms, which are another well-known Maxwell Equations invariant, does it have any practical application?

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I wonder if this was inversion in the sense of special conformal transformations ? – twistor59 Oct 3 '12 at 15:20
Alternately, are you talking about the swapping of the electric and magnetic fields, which is invariant in vacuum, or if you postulate the existence of magnetic densities. – Jerry Schirmer Oct 3 '12 at 15:36
up vote 2 down vote accepted

If you mean special conformal transformation $x\to1/x$, conformal invariance of Maxwell equations is known since 1909. See here: or here:

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Ah, I'm pretty sure that must be what the author was referring to. Many thanks for the references (and to everyone else who has replied) – John R Ramsden Oct 5 '12 at 15:09

Perhaps OP is thinking of electromagnetic duality? For introduction and applications, see e.g. these pdf notes by J.M. Figueroa-O’Farrill.

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