One-loop diagrams of Delbruck scattering

[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?

 

[eljose79]

I understand your confusion and skepticism about the need for the other three diagrams. However, it is important to note that in quantum field theory, all possible diagrams must be taken into account in order to accurately calculate amplitudes. This is because the contributions from the diagrams are not always equal and can lead to different results.

In the case of Delbruck scattering, the additional three diagrams involve virtual particles, which are particles that do not exist as physical particles but are allowed in the calculation of amplitudes. These virtual particles can contribute significantly to the amplitude and cannot be ignored.

Moreover, the other three diagrams involve different momentum configurations and can lead to different results when calculated. This is known as momentum routing and is an important concept in quantum field theory.

In conclusion, while the other three diagrams may seem redundant, they are crucial in accurately calculating the four photon Delbruck scattering amplitude in QED. It is important to consider all possible diagrams in order to obtain a complete and accurate understanding of the physical process.