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In the path integral expression for a Feynman propagator of a spinlessparticle of mass $m$, the path integral amplitude for a path of proper length${\cal R}(x,x'| g_{\mu\nu})$ connecting events $x$ and $x'$ in a spacetimedescribed by the metric tensor $g_{\mu\nu}$ is $\exp-[m {\cal R}(x,x'|g_{\mu\nu})]$. In a recent paper, assuming the path integral amplitude to beinvariant under the duality transformation ${\cal R} \to (L_P^2/{\cal R})$,Padmanabhan has evaluated the modified Feynman propagator in an arbitrarycurved spacetime. He finds that the essential feature of this `principle ofpath integral duality' is that the Euclidean proper distance $(\Delta x)^2$between two infinitesimally separated spacetime events is replaced by $[(\Deltax)^2 + 4L_P^2 ]$. In other words, under the duality principle the spacetimebehaves as though it has a `zero-point length' $L_P$, a feature that isexpected to arise in a quantum theory of gravity. In the Schwinger's propertime description of the Feynman propagator, the weightage factor for a pathwith a proper time $s$ is $\exp-(m^2s)$. Invoking Padmanabhan's `principle ofpath integral duality' corresponds to modifying the weightage factor$\exp-(m^2s)$ to $\exp-[m^2s + (L_P^2/s)]$. In this paper, we use this modifiedweightage factor in Schwinger's proper time formalism to evaluate the quantumgravitational corrections to some of the standard quantum field theoreticresults in flat and curved spacetimes. We find that the extra factor$\exp-(L_P^2/s)$ acts as a regulator at the Planck scale thereby `removing' thedivergences that otherwise appear in the theory. Finally, we discuss the widerimplications of our analysis.Comment: 26 pages, Revte

Hypothesis of path integral duality. II. Corrections to quantum field theoretic results