Could someone clue me in real quick or does this question deserve its own thread: to my understanding, QFT is usually only done perturbatively, and from what I can tell, can only deal with asymptotically free particles. Any bound system as simple as the Hydrogen atom ought to effectively break this approach because an electron trapped forever obviously violates the asymptotic assumption. Has there ever been any progress made for that? My background is QM of bound systems and scattering problems…