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I have to write the matrix element $i\mathcal{M}$ given the Feynman rules of QED for the $\gamma \gamma$ scattering as the example above. Suppose that time is the vertical. There are two times, $t, t'$ such that $t'>t$ with two nodes. I now more or less to write matrix elements with one node at each time, but not with more than one. How should I proceed?

Moreover, there is charge conservation at $t$ and $t'$?

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up vote 3 down vote accepted

If anyone is interested, the answer to my question is

$$i\mathcal{M}=\frac{-ie^4\epsilon_{\eta}(k)\gamma^{\eta}g_{\eta \delta}\gamma^{\delta}\epsilon_{\delta}(k')g_{\delta \beta}\gamma^{\beta}\epsilon^*_{\beta}(k'')g_{\alpha \beta}e^*_{\alpha}(k''')\gamma^{\alpha}g_{\alpha \eta}}{(q^2+i\epsilon)^4}$$  

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