Lagrangian for E and B fields, not vector potential?

by pellman
Tags: fields, lagrangian, potential, vector
pellman is offline
Jun12-10, 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 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?
Phys.Org News Partner Physics news on
Physicists design quantum switches which can be activated by single photons
'Dressed' laser aimed at clouds may be key to inducing rain, lightning
Higher-order nonlinear optical processes observed using the SACLA X-ray free-electron laser
madness is offline
Jun12-10, 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.

Register to reply

Related Discussions
Can all vector fields be described as the vector Laplacian of another vector field? Calculus 5
Lagrangian for fields AND particles? Classical Physics 1
Vector Calc Homework Help! Divergence Free Vector Fields Calculus & Beyond Homework 0
Lagrangian- what potential? Advanced Physics Homework 1
Potential function for conservative vector fields Calculus & Beyond Homework 5