Feynmandiagram

A Feynman diagram, sometimes written as Feynman diagram or, less commonly, as Feynmandiagram, is a graphical representation used in quantum field theory to organize and compute terms in a perturbative expansion of interaction amplitudes. In a diagram, lines denote propagating particles and vertices denote interactions. External lines correspond to incoming or outgoing states, while internal lines represent virtual particles. The arrangement encodes the flow of time and the connectivity of interactions, providing a compact visualization of complex mathematical expressions.

To extract a numerical prediction from a Feynman diagram, one applies the Feynman rules of the underlying theory. Each propagator contributes a specific mathematical factor, each vertex contributes a coupling factor, and symmetry factors account for indistinguishable configurations. One integrates over the momenta of all internal lines, enforcing energy-momentum conservation at each vertex. The resulting expression yields an amplitude, whose modulus squared gives a probability or cross section after summing over final states. Diagrams are organized by perturbative order in the coupling constant, with more complex diagrams typically corresponding to higher-order corrections.

Feynman diagrams have been essential in quantum electrodynamics and the broader Standard Model. A classic tree-level process is electron-positron annihilation into a muon-antimuon pair, mediated by a virtual photon. Loop diagrams introduce quantum corrections that may require regularization and renormalization to handle divergences. Beyond QED, Feynman diagrams underpin calculations in quantum chromodynamics and electroweak theory, serving as a universal bookkeeping tool for perturbative interactions.

Historically introduced by Richard Feynman in the late 1940s, these diagrams simplified the visualization and computation of particle interactions. They are not literal particle paths but represent terms in a perturbative series, valid where the coupling is sufficiently small for the series to be meaningful.