Editing Faddeev–Popov ghost (section)

==Ghost field Lagrangian==
The Lagrangian for the ghost fields <math>c^a(x)\,</math> in [[Yang–Mills theory|Yang–Mills theories]] (where <math>a</math> is an index in the adjoint representation of the [[gauge group]]) is given by
:<math>
\mathcal{L}_{\text{ghost}}=\partial_{\mu}\bar{c}^{a}\partial^{\mu}c^{a}+gf^{abc}\left(\partial^{\mu}\bar{c}^{a}\right)A_{\mu}^{b}c^{c}\;.
</math>
The first term is a [[kinetic term]] like for regular complex scalar fields, and the second term describes the interaction with the [[gauge field]]s as well as the [[Higgs field]]. Note that in ''abelian'' gauge theories (such as [[quantum electrodynamics]]) the ghosts do not have any effect since the [[structure constant]]s <math>f^{abc} = 0</math> vanish. Consequently, the ghost particles do not interact with abelian gauge fields.