 Solution

The anticommuting fields $c$ and $\bar{c}$ represent the field-dependent Faddeev-Popov determinant. They are Lorentz-scalar Grassmann fields, appear only on internal lines, and contribute a minus sign for each closed ghost loop. Their diagrams cancel unphysical gauge-polarization contributions and are required for gauge-independent, unitary amplitudes in a non-Abelian covariant gauge.