Assume we have the abelian gauge theory with single fermion. Suppose the following diagram:
Here the initial "photon" $\gamma$ is in the same state as the final one, so this is the diagram of self-energy. I want to check whether the optical theorem holds for it.
The optical theorem for the total amplitude reads $$ \tag 1 2\text{Im}M_{\gamma \to \gamma}= (2\pi)^{4}\sum_{n}|M_{\gamma \to n}|^{2}\delta (p_{n} - p_{\gamma}) \simeq \Gamma_{\gamma} $$
The question: have I also take into account the diagram which is also 6th order of perturbation theory?
An edit
It seems that the formal answer is indeed yes. Really, the rhs of $(1)$ contains the half of the squared diagram, and the diagram above is needed in the lhs.
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