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

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

  • $\begingroup$ This is pretty much the direct application of the definition of the Hodge dual? $\endgroup$ – Bence Racskó Oct 4 at 22:47
  • $\begingroup$ Can you tell us where exactly are you getting stuck? $\endgroup$ – Amey Joshi Oct 5 at 5:02
  • $\begingroup$ 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. $\endgroup$ – A.V.S. Oct 5 at 6:39

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