If my question sounds ignorant or even insulting, I apologise. I may be completely wrong, since I'm not a theoretical physicist.
So, I understand why perturbation theory was originally used in quantum mechanics and even earlier in other fields. There were just no better ways to solve some problems (at least approximately). And it's a great method for some problems with 'small' perturbations.
But now we have fast computers and advanced numerical methods. But not only do researchers still use PT for particular problems, much of theoretical work in quantum mechanics is still based on first-order (or second-order at best) PT. Take Fermi's golden rule for example.
But PT (first or second order, which are used) does not always give a good approximation, and I even heard that its convergence has not been proven in general.
So please, tell me, is there some work being done on moving beyond PT in the theoretical body of quantum mechanics, solid state physics and other fields? Or maybe, there is some advanced PT with high-order terms better suited to computer implementations?