Editing Wilson loop (section)

===Topological field theory===

In a [[topological quantum field theory|topological field theory]], the expectation value of Wilson loops does not change under smooth deformations of the loop since the field theory does not depend on the [[metric (mathematics)|metric]].<ref>{{cite book|last=Fradkin|first=E.|author-link=Eduardo Fradkin|date=2021|title=Quantum Field Theory: An Integrated Approach|url=|doi=|location=|publisher=Princeton University Press|chapter=22|page=697|isbn=978-0691149080}}</ref> For this reason, Wilson loops are key [[observable]]s on in these theories and are used to calculate global properties of the [[manifold]]. In <math>2+1</math> dimensions they are closely related to [[knot theory]] with the expectation value of a product of loops depending only on the manifold structure and on how the loops are tied together. This led to the famous connection made by [[Edward Witten]] where he used Wilson loops in [[Chern–Simons theory]] to relate their [[partition function (quantum field theory)|partition function]] to [[Jones polynomial]]s of knot theory.<ref>{{cite journal|last1=Witten|first1=E.|authorlink1=Edward Witten|date=1989|title=Quantum Field Theory and the Jones Polynomial|url=http://projecteuclid.org/euclid.cmp/1104178138|journal=Commun. Math. Phys.|volume=121|issue=3|pages=351–399|doi=10.1007/BF01217730|pmid=|arxiv=|bibcode=1989CMaPh.121..351W |s2cid=14951363|access-date=}}</ref>