Duality and Zero-Point Length of Spacetime

Abstract

The action for a relativistic free particle of mass m receives a contribution 2mds 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 ! L2 P yds, 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 sx 2 yd2 to sx 2 yd2 1 L2 P . The implications of this result are discussed.