  I 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.
