Feynman diagram

In <a href="/facts/Theoretical_physics/Cs2Y12rQ">theoretical physics</a>, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of <a href="/facts/Subatomic_particle/tMEzcTWQ">subatomic particles</a>. The scheme is named after American physicist <a href="/facts/Richard_Feynman/32vGFrtB">Richard Feynman</a>, who introduced the diagrams in 1948. 
The calculation of <a href="/facts/Probability_amplitude/ryPgJvs8">probability amplitudes</a> in theoretical particle physics requires the use of large, complicated <a href="/facts/Integral/4PeM0mJc">integrals</a> over a large number of <a href="/facts/Variable_(mathematics)/VbQlrvKz">variables</a>. Feynman diagrams instead represent these integrals graphically.
Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula. According to <a href="/facts/David_Kaiser_(physicist)/dQLs7dFt">David Kaiser</a>, "Since the middle of the 20th century, theoretical physicists have increasingly turned to this tool to help them undertake critical calculations. Feynman diagrams have revolutionized nearly every aspect of theoretical physics." 
While the diagrams apply primarily to <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, they can be used in other areas of physics, such as <a href="/facts/Solid-state_physics/Cmc6hvyR">solid-state theory</a>. <a href="/facts/Frank_Wilczek/EnrB8uUn">Frank Wilczek</a> wrote that the calculations that won him the 2004 <a href="/facts/Nobel_Prize_in_Physics/o6w1nCbr">Nobel Prize in Physics</a> "would have been literally unthinkable without Feynman diagrams, as would [Wilczek's] calculations that established a route to production and observation of the <a href="/facts/Higgs_boson/3LAYXfft">Higgs particle</a>."
A Feynman diagram is a graphical representation of a <a href="/facts/Perturbation_theory_(quantum_mechanics)/lYGgk9Ph">perturbative</a> contribution to the <a href="/facts/Transition_amplitude/ryPgJvs8">transition amplitude</a> or correlation function of a quantum mechanical or statistical field theory. Within the <a href="/facts/Canonical_quantization/AKHX2JQn">canonical</a> formulation of quantum field theory, a Feynman diagram represents a term in the <a href="/facts/Wick%2527s_theorem/36CgXg1u">Wick's expansion</a> of the perturbative <a href="/facts/S-matrix/NffJvlpp">S-matrix</a>. Alternatively, the <a href="/facts/Path_integral_formulation/6lt2MHkW">path integral formulation</a> of quantum field theory represents the transition amplitude as a weighted sum of all possible histories of the system from the initial to the final state, in terms of either particles or fields. The transition amplitude is then given as the matrix element of the S-matrix between the initial and final states of the quantum system.
Feynman used <a href="/facts/Ernst_Stueckelberg/T6vw38Sq">Ernst Stueckelberg</a>'s interpretation of the <a href="/facts/Positron/HgV4zBzA">positron</a> as if it were an <a href="/facts/Electron/L0KBo5cW">electron</a> moving backward in time. Thus, <a href="/facts/Antiparticle/7Ic43ThI">antiparticles</a> are represented as moving backward along the time axis in Feynman diagrams.

Feynman diagram open-in-new

Feynman diagram