Editing Wilson loop (section)

{{Short description|Gauge field loop operator}}
{{Redirect|Wilson line|the Wilson Line shipping company|Thomas Wilson Sons & Co.}}

In [[quantum field theory]], '''Wilson loops''' are [[Introduction to gauge theory|gauge invariant]] operators arising from the [[parallel transport]] of gauge variables around closed [[loop (topology)|loops]]. They encode all gauge information of the theory, allowing for the construction of [[loop representation in gauge theories and quantum gravity|loop representations]] which fully describe [[gauge theory|gauge theories]] in terms of these loops. In pure gauge theory they play the role of [[order operator]]s for [[color confinement|confinement]], where they satisfy what is known as the area law. Originally formulated by [[Kenneth G. Wilson]] in 1974, they were used to construct links and plaquettes which are the fundamental parameters in [[lattice gauge theory]].<ref>{{cite journal|last1=Wilson|first1=K.G.|authorlink1=Kenneth G. Wilson|date=1974|title=Confinement of quarks|url=https://link.aps.org/doi/10.1103/PhysRevD.10.2445|journal=Phys. Rev. D|volume=10|issue=8|pages=2445–2459|doi=10.1103/PhysRevD.10.2445|pmid=|arxiv=|bibcode=1974PhRvD..10.2445W |s2cid=|access-date=|url-access=subscription}}</ref> Wilson loops fall into the broader class of loop [[operator (physics)|operators]], with some other notable examples being [['t Hooft loop]]s, which are magnetic duals to Wilson loops, and [[Polyakov loop]]s, which are the thermal version of Wilson loops.