  Using the recently developed groupoidal description of Schwinger's picture of
Quantum Mechanics, a new approach to Dirac's fundamental question on the role
of the Lagrangian in Quantum Mechanics is provided. It is shown that a function
$\ell$ on the groupoid of configurations (or kinematical groupoid) of a quantum
system determines a state on the von Neumann algebra of the histories of the
system. This function, which we call {\itshape q-Lagrangian}, can be described
in terms of a new function $\mathcal{L}$ on the Lie algebroid of the theory.
When the kinematical groupoid is the pair groupoid of a smooth manifold $M$,
the quadratic expansion of $\mathcal{L}$ will reproduce the standard
Lagrangians on $TM$ used to describe the classical dynamics of particles.
