Editing Feynman diagram (section)

{{Short description|Pictorial representation of the behavior of subatomic particles}}
[[File:Feynmann Diagram Gluon Radiation.svg|class=skin-invert-image|thumb|upright=1.35|In this Feynman diagram, an [[electron]] ('''e<sup>−</sup>''') and a [[positron]] ('''e<sup>+</sup>''') [[Annihilation|annihilate]], producing a [[photon]] ('''γ''', represented by the blue sine wave) that becomes a [[quark]]–[[antiquark]] pair (quark '''q''', antiquark '''q̄'''), after which the antiquark radiates a [[gluon]] ('''g''', represented by the green helix).]]
{{Quantum field theory}}

In [[theoretical physics]], a '''Feynman diagram''' is a pictorial representation of the mathematical expressions describing the behavior and interaction of [[subatomic particle]]s. The scheme is named after American physicist [[Richard Feynman]], who introduced the diagrams in 1948. 

The calculation of [[probability amplitude]]s in theoretical particle physics requires the use of large, complicated [[integral]]s over a large number of [[variable (mathematics)|variable]]s. 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 [[David Kaiser (physicist)|David Kaiser]], "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."<ref name="Kaiser 2005">{{cite journal |last=Kaiser |first=David |year=2005 |title=Physics and Feynman's Diagrams |url=http://web.mit.edu/dikaiser/www/FdsAmSci.pdf |archive-url=https://web.archive.org/web/20120527062956/http://web.mit.edu/dikaiser/www/FdsAmSci.pdf |archive-date=2012-05-27 |url-status=live |journal=[[American Scientist]] |volume=93 |issue=2 |page=156|doi=10.1511/2005.52.957 }}</ref> 

While the diagrams apply primarily to [[quantum field theory]], they can be used in other areas of physics, such as [[solid-state physics|solid-state theory]]. [[Frank Wilczek]] wrote that the calculations that won him the 2004 [[Nobel Prize in Physics]] "would have been literally unthinkable without Feynman diagrams, as would [Wilczek's] calculations that established a route to production and observation of the [[Higgs boson|Higgs particle]]."<ref>{{Cite web|title=Why Feynman Diagrams Are So Important|url=https://www.quantamagazine.org/why-feynman-diagrams-are-so-important-20160705/|access-date=2020-06-16|website=Quanta Magazine|date=5 July 2016|language=en}}</ref>

A Feynman diagram is a graphical representation of a [[Perturbation theory (quantum mechanics)|perturbative]] contribution to the [[transition amplitude]] or correlation function of a quantum mechanical or statistical field theory. Within the [[canonical quantization|canonical]] formulation of quantum field theory, a Feynman diagram represents a term in the [[Wick's theorem|Wick's expansion]] of the perturbative [[S-matrix|{{mvar|S}}-matrix]]. Alternatively, the [[path integral formulation]] 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 {{mvar|S}}-matrix between the initial and final states of the quantum system.

Feynman used [[Ernst Stueckelberg]]'s interpretation of the [[positron]] as if it were an [[electron]] moving backward in time.<ref name="Feynman 1949">{{cite journal |last=Feynman |first=Richard |year=1949 |title=The Theory of Positrons |url=https://authors.library.caltech.edu/3520/ |url-status=dead |journal=Physical Review |volume=76 |issue=6 |pages=749–759 |bibcode=1949PhRv...76..749F |doi=10.1103/PhysRev.76.749 |s2cid=120117564 |archive-url=https://web.archive.org/web/20220809030941/https://authors.library.caltech.edu/3520/ |archive-date=2022-08-09 |access-date=2021-11-12 |quote=In this solution, the 'negative energy states' appear in a form which may be pictured (as by Stückelberg) in space-time as waves traveling away from the external potential backwards in time. Experimentally, such a wave corresponds to a positron approaching the potential and annihilating the electron.|url-access=subscription }}</ref> Thus, [[antiparticle]]s are represented as moving backward along the time axis in Feynman diagrams.