Comment by superposeur

There’s an aspect of path integrals that’s always bugged me. They rely on an underlying classical field configuration space to integrate over. But, this seems problematic to me, since properly the objects of classical physics should emerge as limits of quantum physics. Shouldn’t we be able to start with “pure” quantum mechanics (a state space, a Hamiltonian operator), with no mention even of “paths” and get out classical physics? I.e. it seems backward to speak of a particle trying out different paths since a “path” is a classical notion; it’s as though quantum mechanics is merely a superstructure on top of an underlying classical layer rather than the other way around. Know what I mean?