= Ghost coupling in the Abelian Higgs model
{title2=$\mathcal L_{\rm gh}=-\bar c[\Box+\xi e^2(f+h)^2]c$}
With the specified scalar-dependent <gauge fixing>, the <Faddeev-Popov determinant> depends on the radial <Higgs mode> even though the <gauge group> is Abelian. Besides a ghost <mass> squared $\xi e^2f^2$, the <Lagrangian density> contains $-2\xi e^2fh\bar cc-\xi e^2h^2\bar cc$. These <Faddeev-Popov ghosts> do not decouple for generic $\xi$; their interactions vanish in the $\xi\to0$ <Landau gauge> limit. Free ghosts in pure Abelian <Lorenz gauge> rely on a field-independent determinant, rather than merely on commutativity of the <gauge group>.
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