  In the path integral expression for a Feynman propagator of a spinless
particle 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 spacetime
described 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 be
invariant under the duality transformation ${\cal R} \to (L_P^2/{\cal R})$,
Padmanabhan has evaluated the modified Feynman propagator in an arbitrary
curved spacetime. He finds that the essential feature of this `principle of
path integral duality' is that the Euclidean proper distance $(\Delta x)^2$
between two infinitesimally separated spacetime events is replaced by $[(\Delta
x)^2 + 4L_P^2 ]$. In other words, under the duality principle the spacetime
behaves as though it has a `zero-point length' $L_P$, a feature that is
expected to arise in a quantum theory of gravity. In the Schwinger's proper
time description of the Feynman propagator, the weightage factor for a path
with a proper time $s$ is $\exp-(m^2s)$. Invoking Padmanabhan's `principle of
path 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 modified
weightage factor in Schwinger's proper time formalism to evaluate the quantum
gravitational corrections to some of the standard quantum field theoretic
results 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' the
divergences that otherwise appear in the theory. Finally, we discuss the wider
implications of our analysis.
