Is Epsilon(abcd) F^(ab) F^(cd) a Sensible Electromagnetic Lagrangian?

[deadringer]

We have a suggested Lagrangian

epsilon(abcd) F^(ab) F^(cd)

and are asked to comment if this is a sensible EM Lagrangian. The only thing i can think of is that its still gauge invariant in the normal way but otherwise I am stumped. would appreciate any suggestions. thanks

 

[dextercioby]

Did you compute its field equations ?