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The (Feynman) propagator $G(x_2,x_1)$ encodes the entire dynamics of amassive, free scalar field propagating in an arbitrary curved spacetime. Theusual procedures for computing the propagator -- either as a time orderedcorrelator or from a partition function defined through a path integral --requires introduction of a field $\phi(x)$ and its action functional$A[\phi(x)]$. An alternative, more geometrical, procedure is to define apropagator in terms of the world-line path integral which only uses curves,$x^i(s)$, defined on the manifold. I show how the world-line path integral canbe reinterpreted as an ordinary integral by introducing the concept ofeffective number of quantum paths of a given length. Several manipulations ofthe world-line path integral become algebraically tractable in this approach.In particular, I derive an explicit expression for the propagator $G_{\rmQG}(x_2,x_1)$, which incorporates the quantum structure of spacetime through azero-point-length, in terms of the standard propagator $G_{\rm std}(x_2,x_1)$,in an arbitrary curved spacetime. This approach also helps to clarify theinterplay between the path integral amplitude and the path integral measure indetermining the form of the propagator. This is illustrated with severalexplicit examples.

World-line Path integral for the Propagator expressed as an ordinary integral: Concept and Applications