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  • $\begingroup$ Thanks, that helped a lot. I think I'm almost there now but there remain a term proportional to $[\hat{\Phi}a_{\mu},[\partial_{\nu}\hat{\Phi},\hat{\Phi}]]$ and one with μ,ν interchanged in the calculation of Fμν. Not sure why they should vanish $\endgroup$
    – Othin
    Commented May 21, 2019 at 19:05
  • $\begingroup$ If you pull $a_{\mu}$ out of the commutator and use the first identity, you get something proportional to $(\partial_{[\mu} \hat{\Phi}) a_{\nu]}$. This cancels with a term from $\partial_{[\mu}(a_{\nu]} \hat{\Phi})$. $\endgroup$ Commented May 21, 2019 at 20:17
  • $\begingroup$ Thank you, I had forgotten to differentiate the unit vector in the $a_{\nu}\hat{\Phi}$ terms, so I couldn't get the cancelation. It works now. $\endgroup$
    – Othin
    Commented May 21, 2019 at 20:31