However, the path integral formulation is also extremely important in direct application to quantum field theory, in which the “paths” or histories being considered are not the motions of a single particle, but the possible time evolutions of a field over all space.

Much of the formal study of QFT is devoted to the properties of the resulting functional integral, and much effort (not yet entirely successful) has been made toward making these functional integrals mathematically precise.

— Wikipedia on Path integral formulation

2010.01.25 Monday ACHK