Duality and zero-point length of spacetime

The action for a relativistic free particle of mass m receives a contribution (-)mds from a path of infinitesimal length ds. Using this action in a path integral, one can obtain the Feynman propagator for a spinless particle of mass m. Assuming that the path integral amplitude is invariant under the ''duality'' transformation ds --> L(P)(2)/ds, one can calculate the modified Feynman propagator. I show that this propagator is the same as the one obtained by assuming that quantum effects of gravity lead to modification of the spacetime interval (x - y)(2) to (x - y)(2) + L(P)(2). The implications of this result are discussed.