# Does the LSZ-Reduction Formula work for Photons?

Wikipedia states that:

Although the LSZ reduction formula cannot handle bound states, massless particles and topological solitons

yet S-Matrix Elements, represented by Feynman-diagrams for processes with -in and outgoing photons are part of every book on QFT (I'm encountering these at the moment, bear with me, I didn't yet get accustomed to them).

Is Wikipedia wrong, and one can also state the LSZ-Reduction formula for photons? If so, can somebody provide a source to a derivation? (Schwartz only contains a derivation for scalars and fermions).

In case Wikipedia is wrong, why would somebody state something like the citation from wikipedia? Are there subleties?

• Jul 2, 2021 at 12:27
• (Also, see Srednicki, chapter 56 for the derivation) Jul 2, 2021 at 13:15
• The Wikipedia statement is probably referring to IR divergences Jul 3, 2021 at 14:38

In QED the regularisation is rather straightforward. We can simply add a photon mass $$\lambda$$ to the theory. This means that for $$\lambda > 0$$ the LSZ formula actually applies. The IR divergences manifest as terms which diverge when $$\lambda$$ goes to zero.