  A novel derivation of Feynman's sum-over-histories construction of the
quantum propagator using the groupoidal description of Schwinger picture of
Quantum Mechanics is presented. It is shown that such construction corresponds
to the GNS representation of a natural family of states called
Dirac-Feynman-Schwinger (DFS) states. Such states are obtained from a
q-Lagrangian function $\ell$ on the groupoid of configurations of the system.
The groupoid of histories of the system is constructed and the q-Lagrangian
$\ell$ allow to define a DFS state on the algebra of the groupoid. The
particular instance of the groupoid of pairs of a Riemannian manifold serves to
illustrate Feynman's original derivation of the propagator for a point particle
described by a classical Lagrangian $L$.
