Minimal length and small scale structure of spacetime

Many generic arguments support the existence of a minimum spacetime interval L₀. Such a ``zero-point'' length can be naturally introduced in a locally Lorentz invariant manner via Synge's world function biscalar Ω(p,P) which measures squared geodesic interval between spacetime events p and P. I show that there exists a nonlocal deformation of spacetime geometry given by a disformal coupling of metric to the biscalar Ω(p,P), which yields a geodesic interval of L₀ in the limit p→P. Locality is recovered when Ω(p,P)L₀²/2. I discuss several conceptual implications of the resultant small-scale structure of spacetime for QFT propagators as well as spacetime singularities.