In QFT, we can expand the propagator and obtain the diagrammatic expansion to build up the Green's function. If we have a hamiltonian of the type [tex] H = H_{0}+V[/tex], where V is the perturbation, we can build up the Feynman diagrams,and if we could build up all of them to infinite order, we would obtain the exact Green's function on the model.(adsbygoogle = window.adsbygoogle || []).push({});

However, my question is related with the fact that, in all the formal development of the diagrammatic expansion, V is not assumed to be "small" compared with H0, I mean is a perturbation which in principle is always assumed to be small respect to H0. But what happens if V becomes larger and of the same magnitude as H0? If we go to infinite order of perturbation, do we still have the exact Green's function of the problem?

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# Perturbation theory in strong interaction regime

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