Thanks, obviously
E^2-B^2 is not the right Lagrangian.
My question was more:
Is there any Lagrangian at all in terms of E and B,
no matter how awkward it looks?
Today a colleague explained me that
experimentally the Aharonov-Bohm effect showed
that the real physical can only be...
Typically the action for E-M is
F_{\mu\nu}F^{\mu \nu}
where
F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu
since the equations of motion for
A_{\mu}
are the inhomogenous Maxwell equations.
However, here comes my problem:
If one expresses this action in terms of the electric and...