What are "functionals" and "functional integrals"?
What is a functional? One says that a functional is given if a rule is fixed that associates a number to every function from certain function family. Thus, it is a mapping from a set of functions to a set of numbers. It is a generalization of the idea of a function of several variables to the realm of a function of infinitely many variables, the values of the argument function. For example, $sin(x^2)$ is not a functional. On the other hand ...