= Faddeev-Popov ghost
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{wiki=Faddeev–Popov_ghost}
= Faddeev-Popov ghost field
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{synonym}
= FP ghost
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{synonym}
A Faddeev-Popov ghost is an auxiliary <Grassmann-valued field> transforming as a <scalar field> introduced to express the <Faddeev-Popov determinant> as a <functional integral>. Its anticommuting variables reproduce a determinant rather than the inverse determinant associated with an ordinary commuting <scalar field>.
In a non-Abelian <covariant gauge>, the <Faddeev-Popov operator> depends on the <gauge field>, giving ghost interaction vertices and <ghost loops>. These contributions are required for consistent cancellation of unphysical gauge-polarization effects. Ghosts are not physical asymptotic <particles>, so their scalar transformation and anticommuting variables do not contradict the <Spin-statistics theorem> for physical states. In an Abelian linear gauge with a field-independent determinant, the ghosts decouple; that simplification need not hold for every nonlinear gauge condition.
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