Faddeev-Popov operator ($\mathcal{M}=\delta \chi [A+D\omega ]/\delta \omega {|}_{\omega =0}$)

For a gauge condition $\chi [A]=0$, the linearization of $\chi [A+D\omega ]$ in the gauge parameter is the Faddeev-Popov operator. Its determinant is represented by Faddeev-Popov ghost fields.