I'm trying to prove the conformal invariance (under [itex]g_{\mu\nu}\to\omega^2 g_{\mu\nu}[/itex]) of(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\bar{\Box}{\bar{\phi}}+\frac{1}{4}\frac{n-2}{n-1}\bar{R}\bar{\phi}

[/tex]

I've found that this equation is invariant upto a quantity proportional to

[tex]

g^{\mu\nu}\left[-\omega(\nabla_{\mu}\nabla_{\nu}\omega)\phi+(\omega^2-\omega)(\nabla_{\mu}\omega)(\nabla_{\nu} \phi)-\frac{n-4}{4}(\nabla_{\mu}\omega)(\nabla_{\nu} \phi)\right]

[/tex]

Here [itex]\bar{\phi}=\omega^{(2-n)/2}\phi[/itex], and the conformal transformations of other quantitities like box and the Ricci scalar are those found in Carroll Appendix.

How can I get rid of this extra unwanted quantity? (or have I simply made an algebraic error of some kind)

Thanks

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# Conformal inv of scalar wave equation

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