As R.Feynman has shown to F. Dyson - who published it then in 1990 under
the name of "Feynman's
proof of Maxwell's equations" - the only interactions compatible
with the canonical uncertainty relation (for scalar particles
on flat $\R^3$) are the Lorentz covariant electromagnetic interactions.
We generalize Feynman's argument to arbitrary configuration spaces, thereby
clarifying its hidden assumptions as well as its geometrical significance.
In addition, our result establishes a correspondence between globally
hyperbolic spacetimes and
solutions to our (algebraically formulated) axioms for nonrelativistic
quantum mechanics.