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**1. Homework Statement**

In order to determine the infinitesimal generators of the conformal group we consider an infinitesimal coordinate transformation:

[itex]x^{\mu} \to x^\mu+\epsilon^\mu[/itex]

We obtain [itex]\partial_\mu\epsilon_\nu+\partial_\nu\epsilon_\mu=\frac{2}{d}(\partial\cdot\epsilon)\eta_{\mu\nu}[/itex] where d is the dimension of spacetime.

Derive [itex](\eta_{\mu\nu}\Box+(d-2)\partial_\mu \partial_\nu)\partial\cdot\epsilon=0[/itex]

**2. Homework Equations**

[itex]\eta_{\mu\nu}\eta^{\mu\nu}=d[/itex]

**3. The Attempt at a Solution**

I think I am really close to the solution, but somehow I don't arrive there.

[itex]\partial_\mu\epsilon_\nu+\partial_\nu\epsilon_\mu=\frac{2}{d}(\partial\cdot\epsilon)\eta_{\mu\nu}[/itex]

[itex]\Rightarrow \partial^\nu\partial_\mu\epsilon_\nu+\partial^\nu{\partial}_\nu\epsilon_\mu=\frac{2}{d}\partial^\nu({\partial}\cdot\epsilon)\eta_{\mu\nu}[/itex]

[itex]\Rightarrow \partial_\mu(\partial\cdot\epsilon)+\Box{\epsilon}_\mu=\frac{2}{d}\partial_\mu(\partial\cdot\epsilon)[/itex]

[itex]\Rightarrow (d-2)\partial_\mu(\partial\cdot\epsilon)+d\cdot{\Box}{\epsilon}_\mu=0[/itex]

[itex]\Rightarrow (d-2)\partial_\mu\partial_\nu(\partial\cdot\epsilon)+d\partial_\nu\Box{\epsilon}_\mu=0[/itex]

I think I need to use [itex]d=\eta_{\mu\nu}\eta^{\mu\nu}[/itex] now, but I don't get the right result.

Can somebody help me?

Best regards, physicus