Editing Quantum field theory (section)

===Perturbative and non-perturbative methods===
Using [[perturbation theory (quantum mechanics)|perturbation theory]], the total effect of a small interaction term can be approximated order by order by a series expansion in the number of [[virtual particle]]s participating in the interaction. Every term in the expansion may be understood as one possible way for (physical) particles to interact with each other via virtual particles, expressed visually using a [[Feynman diagram]]. The [[electromagnetic force]] between two electrons in QED is represented (to first order in perturbation theory) by the propagation of a virtual photon. In a similar manner, the [[W and Z bosons]] carry the weak interaction, while [[gluon]]s carry the strong interaction. The interpretation of an interaction as a sum of intermediate states involving the exchange of various virtual particles only makes sense in the framework of perturbation theory. In contrast, non-perturbative methods in QFT treat the interacting Lagrangian as a whole without any series expansion. Instead of particles that carry interactions, these methods have spawned such concepts as [['t Hooft–Polyakov monopole]], [[domain wall]], [[flux tube]], and [[instanton]].<ref name="shifman">{{cite book |last=Shifman |first=M. |author-link=Mikhail Shifman |date=2012 |title=Advanced Topics in Quantum Field Theory |publisher=Cambridge University Press |isbn=978-0-521-19084-8 }}</ref> Examples of QFTs that are completely solvable non-perturbatively include [[Minimal model (physics)|minimal models]] of [[conformal field theory]]<ref>{{cite book |last1=Di Francesco |first1=Philippe |last2=Mathieu |first2=Pierre |last3=Sénéchal |first3=David |date=1997 |title=Conformal Field Theory |publisher=Springer |isbn=978-1-4612-7475-9 |url=https://books.google.com/books?id=5u7jBwAAQBAJ }}</ref> and the [[Thirring model]].<ref>{{Cite journal |last=Thirring |first=W. |author-link=Walter Thirring |year=1958 |title=A Soluble Relativistic Field Theory? |journal=[[Annals of Physics]] |volume=3 |issue=1|pages=91–112 |bibcode=1958AnPhy...3...91T |doi=10.1016/0003-4916(58)90015-0}}</ref>