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Consider the set of 1PI diagrams with three external photons.

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It is apparent that there are no tree-level diagrams for this process.

  1. What are the possible one-loop diagrams for this process? Why do the different one-loop diagrams involve simply an interchange of the Lorentz indices and photon momenta?

  2. Should this diagram be interpreted as a $1 \to 2$ scattering or a $2 \to 1$ scattering?

  3. What about $4$-photon scattering? Should a $4$-photon scattering be thought of as a $1 \to 3$, $2 \to 2$ or $3 \to 1$ scattering?

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  • $\begingroup$ 1. What do you think? 2. & 3. What's the difference between $2\to 1$ and $1\to 2$ given that the S-matrix is unitary? Why do you think this information is encoded in the diagrams? $\endgroup$ – ACuriousMind Feb 15 '17 at 21:53
  • $\begingroup$ 1. The different Lorentz indices label the different photons. But, I am not sure why this means that their momenta should be exchanged. Of course, this is analogous to the explanation of the $t$ and $u$ channel diagrams, but that interchange of momenta confuses me too. $\endgroup$ – nightmarish Feb 15 '17 at 21:56
  • $\begingroup$ 2. The S-matrix is unitary, which means that probability is conserved. How does this imply that the amplitude is invariant under time-reversal? $\endgroup$ – nightmarish Feb 15 '17 at 21:58

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