The SE should be a non-relativistic limit of whatever model is the next step. Not sure if it requires a formalization of QFT, it just needs to make decent predictions. Physicists are not overly picky. As long as it’s reasonably self-consistent. Or not even. As long as it helps you calculate something new and interesting unambiguously.
QFT IS the obvious next-step, but the reason people play with standard quantum formulations instead of trying to work in the context of QFT and ‘push the interpretation down’ is that QFT isn’t yet on firm footing.
The SE should be a non-relativistic limit of whatever model is the next step. Not sure if it requires a formalization of QFT, it just needs to make decent predictions. Physicists are not overly picky. As long as it’s reasonably self-consistent. Or not even. As long as it helps you calculate something new and interesting unambiguously.
QFT IS the obvious next-step, but the reason people play with standard quantum formulations instead of trying to work in the context of QFT and ‘push the interpretation down’ is that QFT isn’t yet on firm footing.