Faddeev-Popov determinant (${\Delta }_{\mathrm{FP}}$)

The Faddeev-Popov determinant is the functional Jacobianthat compensates for the change from integration along a gauge orbit to a gauge-fixing condition $G(A)=0$. It can be represented by a path integral over a Faddeev-Popov ghost field pair.

A Faddeev-Popov ghost field is a Grassmann-valued scalar field whose Gaussian functional integral represents the Faddeev-Popov determinant. Ghosts occur only on internal lines and cancel unphysical gauge-field contributions.