Feynman Path Integral

Quantum Field Theory · 1948

Equation: ⟨x_f|x_i⟩ = ∫Dx·e^(iS[x]/ℏ)
Field: Quantum Field Theory
Named After: Richard Feynman
Year: 1948

Symbols

⟨x_f|x_i⟩ amplitude to go from one point to another · ∫Dx a sum over every conceivable path between them · S[x] the classical action along each path · ℏ sets the scale of quantum interference

Significance

A particle takes every possible path at once, each contributing a spinning phase — most cancel, and what survives is what we observe. When ℏ is small the stationary-action path wins, which is why classical mechanics' least-action principle works at all. The computational engine of modern QFT, from Feynman diagrams to lattice simulations.