Also, we know that QM (as it stands) doesn't have a good way to deal with topological effects and their (low-energy) contributions to various things. TQFTs in 3

Also, we know that QM (as it stands) doesn't have a good way to deal with topological effects and their (low-energy) contributions to various things. TQFTs in 3+1D are an active area of research. Heck, TQFTs in 2+1D are still under active research (and are behind Microsoft's quantum computer efforts).