Feynmandiagrammer

Feynmandiagrammer, commonly known as Feynman diagrams, are graphical representations used in quantum field theory to organize and compute terms in perturbation theory. They were developed by Richard Feynman in the late 1940s and have become a standard tool across particle physics and related fields. The diagrams provide a visual shorthand for complex integrals that describe particle interactions and transitions.

A diagram consists of lines and vertices. Lines represent propagating fields or particles, with different styles often used to distinguish fermions, gauge bosons, and scalar fields. Vertices are points where lines meet and encode interactions dictated by the theory’s Lagrangian. External lines correspond to incoming or outgoing particles in a process, while internal lines represent virtual particles that are integrated over in calculations. Each diagram encodes a specific mathematical term, and the full calculation involves summing over all diagrams that contribute to a given process at a chosen order in the coupling constants.

Calculating with Feynman diagrams involves applying theory-specific Feynman rules. These rules prescribe the mathematical expressions for propagators, vertex factors, and the integration over internal momenta. The resulting amplitude is combined with other diagrams to obtain probabilities for processes, such as scattering cross sections or decay rates. Diagrams are organized by order and topology, with loop diagrams representing quantum corrections.

Feynman diagrams are central to contemporary high-energy physics and many-body theory. They offer intuition about conservation laws and gauge invariance, while serving as a practical bookkeeping method for perturbative calculations. Limitations include reliance on a perturbative expansion, potential divergences requiring regularization and renormalization, and limited applicability in strong-coupling or non-perturbative regimes.