Sum Over Histories

CORE DEFINITION

Developed by Richard Feynman, the path integral formulation treats the amplitude for a particle to travel from one point to another as a sum over every possible trajectory, each weighted by the exponential of its action divided by the reduced Planck constant. Classical paths emerge because contributions from neighboring paths interfere constructively where the action is stationary, while others cancel. The framework extends to quantum field theory, where it underlies Feynman diagrams and perturbation expansions. Key qualification: the path integral is a computational representation of amplitudes, not a claim that a particle literally traverses every route.