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I have to give a lecture about supersymmetry, so I started reading Weinbergs quantum theory of fields vol 3, which is quite of a task. Sometimes I've trouble with some of his conclusions, and I hope you could help me there.

I really do not understand how he got to the formula on top of page 78 (I've got the paperback version from 2005. there is no number, so I post the page). To write it down, this one here.

[tex] \left[f(\Phi)\right]_{\theta_L^2} =& \sum_{nm} \left( \theta^T_L \varepsilon \psi_{nL} (x) \right) \left( \theta^T_L \varepsilon \psi_{mL}(x) \right) \frac{\partial^2 f \left( \phi(x)\right)}{\partial\phi_n(x) \partial\phi_m(x)} \\

&+ \sum_n \mathcal{F}_n(x) \frac{\partial f\left( \phi(x)\right)}{\partial \phi_n(x)} \left( \theta^T_L \varepsilon \theta_L \right)

[/tex]

I think it has to be some kind of series, but I really cant calculate this. So it would be really great if someone could post the calculation of this formula.

Eisenhorn

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# Supersymmetry Weinberg Vol. 3

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