I’ve seen people say that if the coupling constant is large, we can’t trust Feynman Diagrams (like in the case of QCD). The logic is that high couplings describe bound states, whereas Feynman Diagrams describe scattering states, but this argument is not completely satisfactory, since it doesn’t prove that the perturbation series for a large coupling will give an inherently wrong result.
So why can’t we use Feynman Diagrams for a large coupling?
Feynman diagrams are a graphical interpretation of some perturbation series. For those to be defined, you have to consider a parameter to be small, usually the coupling. In a large coupling context there are several approaches possible. You can e.g. still consider the coupling small, and perform high order expansions in the Feynman diagrams, followed by ressumations techniques (keywords: Padé/Borel resumation techniques) to extrapolate your results for high coupling (this is usually very hard). Or you can choose another parameter to be the perturbative one (keyword: large N expansions). Or lastly, abandon Feynman diagrams and use your favorite self-consistent / non pertubative technique.
