  We prove that invariance of a quantum theory under the semiclassical vs.
strong-quantum duality $S/\hbar\longleftrightarrow\hbar/S$, where S is the
classical action, is equivalent to noncommutativity (of the Heisenberg-algebra
type) of the coordinates of the space on which S is defined. We place these
facts in correspondence with gerbes and Neveu-Schwarz B-fields and discuss
their implications for a quantum theory of gravity. Feynman's propagator turns
out to be closely related to the trivialisation of a gerbe on configuration
space.
