2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51955I propose to formalize quantum theories as topological quantum field theories in a generalized sense, associating state spaces with boundaries of arbitrary (and possibly finite) regions of space-time. I further propose to obtain such ``general boundary'' quantum theories through a generalized path integral quantization. I show how both, non-relativistic quantum mechanics and quantum field theory can be given a ``general boundary'' formulation. Surprisingly, even in the non-relativistic case, features normally associated with quantum field theory emerge from consistency conditions. This includes states with arbitrary particle number and pair creation. I also note how three dimensional quantum gravity is an example for a realization of both proposals and suggest to apply them to four dimensional quantum gravity.5 pages, 2 figures, LaTeX + revtex4 + eps; abstract shortened, other minor corrections, references updatedHigh Energy Physics - TheoryGeneral Relativity and Quantum CosmologyQuantum Physicstext