A functional G[f] is a map from a space of functions to a set of numbers. For instance, the action functional S[q] for a particle in one dimension maps the coordinate q(t), which is a function of the time t, into a number – the action of the process. If the particle has mass m and is moving slowly and freely, then for the interval (t1, t2) its action is
If the particle is moving in a potential V(q(t)), then its action is
15.2 Functional derivatives
A functional derivative ...