1996/08/28 by T. Padmanabhan · 1 citation
Physics and Astronomy · #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevlett.78.1854
published as Phys.Rev.Lett. 78 (1997) 1854-1857 · Revtex document; 4 pages
arxiv created 1996/08/28 · arxiv updated 2009/11/30
The action for a relativistic free particle of mass m receives a contribution -mds from a path segment of infinitesimal length ds. Using this action in a path integral, one can obtain the Feynman propagator for a spinless particle of mass m. If one of the effects of quantizing gravity is to introduce a minimum length scale LP in the spacetime, then one would expect the segments of paths with lengths less than LP to be suppressed in the path integral. Assuming that the path integral amplitude is invariant under the `duality' transformation ds→ LP2/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 leads to modification of the spacetime interval (x-y)2 to (x-y)2+LP2. This equivalence suggests a deep relationship between introducing a `zero-point-length' to the spacetime and postulating invariance of path integral amplitudes under duality transformations.