(Richard) Feynman diagrams are symbolic notation tools to understand scattering calculations in quantum particle physics. Diagrams show amplitudes of intermediate states of perturbative expansion (or Dyson series) in experiments, represented according to Feynman rules. Incoming/outgoing lines are constraints on energy, momentum and spin, moving from past to future. Used in quantum electrodynamics and statistical mechanics to show electrons, positrons, virtual photons, quark-antiquark pairs, gluons .... A perennial favorite.
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