# Action in Electromagnetism expressed in differential geometry and tensor notation

$$S = -\frac{1}{4} \int F_{\mu\nu}F^{\mu\nu} = -\frac{1}{2} \int F \wedge *F$$

Trying to figure out why this identity holds true and getting stuck.

• This is pretty much the direct application of the definition of the Hodge dual? – Bence Racskó Oct 4 at 22:47
• Can you tell us where exactly are you getting stuck? – Amey Joshi Oct 5 at 5:02
• Note, that tensor notation expression has an error: the measure of integration is omitted (usually written as $\sqrt{|g|} d^4 x$). This should help. – A.V.S. Oct 5 at 6:39