# A One-loop diagrams of Delbruck scattering

1. Feb 15, 2017

### Bala Tala

I would like to draw the one-loop diagrams for four photon Delbruck scattering amplitude in QED.

Here are the three one-loop diagrams that contribute to the scattering amplitude.

There are three more one-loop diagrams that contribute to the amplitude.
However, I cannot find the other diagrams.

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Here is my tabulation of how the external photons lines are connected using propagators. Here, $p_1$ and $p_2$ are the incoming momenta and $k_1$ and $k_2$ are the outgoing momenta and $\leftrightarrow$ represents a propagator.

$p_{1} \leftrightarrow p_{2} \qquad k_{1} \leftrightarrow k_{2} \qquad p_{1} \leftrightarrow k_{1} \qquad p_{2} \leftrightarrow k_{2}$

$p_{1} \leftrightarrow p_{2} \qquad k_{1} \leftrightarrow k_{2} \qquad p_{1} \leftrightarrow k_{2} \qquad p_{2} \leftrightarrow k_{1}$

$p_{1} \leftrightarrow k_{1} \qquad p_{2} \leftrightarrow k_{2} \qquad p_{1} \leftrightarrow k_{2} \qquad p_{2} \leftrightarrow k_{1}$

This happens to exhaust all possible pairings of external photon lines with propagators. However, three more one-loop diagrams still remain. I know other three one-loop diagrams give the same amplitudes as those above. So, why should be treat the other three diagrams as distinct from the ones drawn above?

2. Feb 23, 2017