Editing Faddeev–Popov ghost (section)

==Appearance in Feynman diagrams==
In [[Feynman diagram]]s, the ghosts appear as closed loops wholly composed of 3-vertices, attached to the rest of the diagram via a gauge particle at each 3-vertex. Their contribution to the [[S matrix|S-matrix]] is exactly cancelled (in the [[Feynman gauge|Feynman–'t Hooft gauge]]) by a contribution from a similar loop of gauge particles with only 3-vertex couplings or gauge attachments to the rest of the diagram.{{efn|Feynman discovered empirically that "boxing" and simply dismissing these diagrams restored unitarity. "''Because, unfortunately, I also discovered in the process that the trouble is present in the Yang−Mills theory; and, secondly, I have incidentally discovered a tree−ring connection which is of very great interest and importance in the meson theories and so on. And so I'm stuck to have to continue this investigation, and of course you appreciate that this is the secret reason for doing any work, no matter how absurd and irrational and academic it looks: we all realize that no matter how small a thing is, if it has physical interest and is thought about carefully enough, you're bound to think of something that's good for something else.''"<ref>{{Cite journal |last=Feynman |first=R.P. |author-link=Richard Feynman |year=1963 |title=Quantum Theory of Gravitation |journal=[[Acta Physica Polonica]] |volume=24 |pages=697−722}}</ref>}} (A loop of gauge particles not wholly composed of 3-vertex couplings is not cancelled by ghosts.) The opposite sign of the contribution of the ghost and gauge loops is due to them having opposite fermionic/bosonic natures. (Closed fermion loops have an extra&nbsp;−1 associated with them; bosonic loops don't.)