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Lagrangian for E and B fields, not vector potential?

by pellman
Tags: fields, lagrangian, potential, vector
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Jun12-10, 07:46 AM
P: 582
Anyone know of a Lagrangian given in terms of E and B (or equivalently the tensor F) that yields Maxwell equations? A link or reference would be appreciated.

I can write down such a Lagrangian which yields the two second-order Maxwell equations, but not the usual four 1st order equations. And I'm not sure: are the second order equations equivalent to the first order form?
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Jun12-10, 08:11 AM
P: 611
[tex] L=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} [/tex]

But then F is defined in terms of (the derivatives of) the potential, not E and B.

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