For 10 points, name this quantity that, like time in Fermat's principle, is stationary for any trajectory taken by a system according to its namesake principle.
The Hilbert form of this quantity can be used to derive Einstein's field equations. The contribution of a path has phase proportional to this quantity in Feynman's path-integral formulation. This quantity appears as Hamilton's principal function in the Hamilton-Jacobi equation. By defining this quantity as the integral of momentum with respect to the generalized position, the path of motion can be found, though not as a function of time. Its variation is zero only if the (*) Lagrangian satisfies the Euler-Lagrange equations. It is given by the integral of the Lagrangian with respect to time in Hamilton's principle. For 10 points, name this quantity that, like time in Fermat's principle, is stationary for any trajectory taken by a system according to its namesake principle.
The Hilbert form of this quantity can be used to derive Einstein's field equations.
action