- #1
Malamala
- 299
- 26
Hello! In Schwarz's QFT, Chapter 24.3 there is a theorem stating that Green's functions have poles when on-shell intermediate particles can be produced. I am not sure I understand how this works. If we have $$e^+e^- \to \gamma^* \to \mu^+\mu^-$$ we can have a positronium as an intermediate state. So when calculating the S matrix for this scattering we should have a term of the form $$\frac{1}{p^2-m_{positronium}^2}$$ but the only fraction appearing in this reaction is the photon propagator which is (in a renormalized theory) of the form $$\frac{1}{p^2(1+\Pi(p^2))}$$ which doesn't necessary have a pole at the positronium mass. I assume that I am missing something. Can someone explain this to me please? Thank you!