Lagrangian for E and B fields, not vector potential?by pellman Tags: fields, lagrangian, potential, vector 

#1
Jun1210, 07:46 AM

P: 565

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 secondorder 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? 



#2
Jun1210, 08:11 AM

P: 606

[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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