  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.
