  We frame the issue of pedestrian dynamics modeling in terms of
path-integrals, a formalism originally introduced in quantum mechanics to
account for the behavior of quantum particles, later extended to quantum field
theories and to statistical physics. Path-integration enables a
trajectory-centric representation of the pedestrian motion, directly providing
the probability of observing a given trajectory. This appears as the most
natural language to describe the statistical properties of pedestrian dynamics
in generic settings. In a given venue, individual trajectories can belong to
many possible usage patterns and, within each of them, they can display wide
variability.
  We provide first a primer on path-integration, and we introduce and discuss
the path-integral functional probability measure for pedestrian dynamics in the
diluted limit. As an illustrative example, we connect the path-integral
description to a Langevin model that we developed previously for a particular
crowd flow condition (the flow in a narrow corridor). Building on our previous
real-life measurements, we provide a quantitatively correct path-integral
representation for this condition. Finally, we show how the path-integral
formalism can be used to evaluate the probability of rare-events (in the case
of the corridor, U-turns).
