  The hypothesis of path integral duality provides a prescription to evaluate
the propagator of a free, quantum scalar field in a given classical background,
taking into account the existence of a fundamental length, say, the Planck
length, $\lp$, in a {\it locally Lorentz invariant manner}. We use this
prescription to evaluate the duality modified propagators in spacetimes with
{\it constant curvature} (exactly in the case of one spacetime, and in the
Gaussian approximation for another two), and show that: (i) the modified
propagators are ultra violet finite, (ii) the modifications are {\it
non-perturbative} in $\lp$, and (iii) $\lp$ seems to behave like a `zero point
length' of spacetime intervals such that $\l< \sigma^2(x,x')\r> =
\l[\sigma^{2}(x,x')+ {\cal O}(1) \lp^2 \r]$, where $\sigma(x,x')$ is the
geodesic distance between the two spacetime points $x$ and $x'$, and the
angular brackets denote (a suitable) average over the quantum gravitational
fluctuations. We briefly discuss the implications of our results.
