= Ghost coupling in a linear Cartesian Abelian Higgs gauge
{title2=$\mathcal L_{\mathrm{gh}}=\bar c\Box c-\xi g^2v(v+h)\bar cc$}
For $D_\mu=\partial_\mu-igA_\mu$, transformations $\delta A_\mu=-\partial_\mu\theta$, $\delta\phi=-ig\theta\phi$, and Cartesian shift $\phi=(v+h+ib)/\sqrt2$, the <Gauge fixing>[gauge function] $G=\partial\cdot A-\xi gvb$ varies by $[-\Box+\xi g^2v(v+h)]\theta$. Exponentiating the <Faddeev-Popov determinant> with the convention $-\bar c(\delta G/\delta\theta)c$ gives <Faddeev-Popov ghost>[ghost mass] squared $\xi g^2v^2$ and one <Ghost coupling in a linear Cartesian Abelian Higgs gauge>[Higgs-ghost] <vertex> $-i\xi g^2v$. A scalar-dependent <Abelian group>[Abelian] gauge therefore has interacting <Faddeev-Popov ghosts>[ghosts]; a pure linear <Lorenz gauge> has a field-independent <determinant>.
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