The Euler equations of motion for a system are derived by applying a variational statement relevant to this quantity; that statement is Hamilton's principal, according to which this quantity is stationary with respect to a particle's path.
The weight of a path in a Feynman path integral is given by e to the i over h-bar times this variable for the path. So-called angles named for this quantity have conjugate momenta given by the closed path integral of a naive momentum with respect to its conjugate coordinate. Hamilton's characteristic function is given by total energy times time plus this quantity. The Euler equations of motion for a system are derived by applying a variational statement relevant to this quantity; that statement is Hamilton's principal, according to which this quantity is stationary with respect to a particle's path. For 10 points, name this quantity, the time integral of the Lagrangian, which is classically minimized for a system's path.
The weight of a path in a Feynman path integral is given by e to the i over h-bar times this variable for the path.
the {action} [prompt on {S}]