# Local construction of Maxwell's action

1. Dec 10, 2014

### gentsagree

What do we mean by "there is no local construction for an action in terms of $F^{\mu\nu}$, or E and B"?

So, I understand the construction "on-shell", once we solve Maxwell's equations to find $F^{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$, and how we can then write an action which is both gauge and Lorentz invariant.

But before we know anything about gauge symmetry, which comes about once we solve for F and express it in terms of A, what tells us that our action in not good enough (i.e. there is no local action to be constructed)?

Thanks

2. Dec 15, 2014