FeynmanDiagramme

FeynmanDiagramme are pictorial representations used in quantum field theory to visualize and organize calculations of particle interactions within perturbation theory. They are a German-language counterpart to the English term Feynman diagrams and are typically described using Feynman rules that translate each diagram into a mathematical expression for a scattering amplitude or decay rate.

In a FeynmanDiagramme, lines represent propagating particles: solid lines with arrows describe fermions, wavy lines denote photons or other gauge bosons, and curly or gluon lines represent gluons. Interaction points, called vertices, encode fundamental couplings from the theory’s Lagrangian. Time is usually illustrated horizontally or vertically, with the convention that external lines correspond to incoming or outgoing particles. Diagrams are not literal particle paths but mnemonic devices that tally the terms arising in a perturbative expansion.

Diagrams contribute to physical quantities such as cross sections and decay rates. Each diagram is assigned a complex amplitude through specific rules, including propagators for internal lines, vertex factors, symmetry factors, and integrals over unobserved momenta. The sum of all diagrams up to a given order yields the observable prediction, subject to renormalization in the presence of infinities.

Historically, FeynmanDiagramme reflect the work of Richard Feynman in the late 1940s. They quickly became a standard tool in quantum electrodynamics and, later, in quantum chromodynamics and the electroweak theory. Limitations include reliance on perturbation theory and difficulties with non-perturbative phenomena.