Editing Virtual particle (section)

== Feynman diagrams ==
[[File:Momentum exchange.svg|thumb|right|One particle exchange scattering diagram]]
The calculation of [[scattering amplitude]]s in theoretical [[particle physics]] requires the use of some rather large and complicated integrals over a large number of variables. These integrals do, however, have a regular structure, and may be represented as [[Feynman diagram]]s.  The appeal of the Feynman diagrams is strong, as it allows for a simple visual presentation of what would otherwise be a rather arcane and abstract formula. In particular, part of the appeal is that the outgoing legs of a Feynman diagram can be associated with actual, [[on-shell]] particles. Thus, it is natural to associate the other lines in the diagram with particles as well, called the "virtual particles".  In mathematical terms, they correspond to the [[propagator]]s appearing in the diagram.

In the adjacent image, the solid lines correspond to actual particles (of momentum p<sub>1</sub> and so on), while the dotted line corresponds to a virtual particle carrying [[momentum]] ''k''. For example, if the solid lines were to correspond to [[electron]]s interacting by means of the [[electromagnetic interaction]], the dotted line would correspond to the exchange of a virtual [[photon]].  In the case of interacting [[nucleon]]s, the dotted line would be a virtual [[pion]]. In the case of [[quark]]s interacting by means of the [[strong force]], the dotted line would be a virtual [[gluon]], and so on.
[[File:Vacuum polarization.svg|thumb|right|One-loop diagram with fermion propagator]]

Virtual particles may be [[meson]]s or [[vector boson]]s, as in the example above; they may also be [[fermion]]s. However, in order to preserve quantum numbers, most simple diagrams involving fermion exchange are prohibited. The image to the right shows an allowed diagram, a [[one-loop diagram]]. The solid lines correspond to a fermion propagator, the wavy lines to bosons.