= Quadratic Abelian gauge fixing
{title2=$F[A]=\partial\cdot A+A^2$}
For $\delta A_\mu=\partial_\mu\omega$, the real quadratic gauge functional varies by $(\Box+2A\cdot\partial)\omega$. Its <Faddeev-Popov operator> depends on the <gauge field>, producing a ghost-gauge vertex even in an <Abelian gauge theory>. With $\Psi=\int\bar c(F[A]+\xi h/2)$, a consistent left <BRST symmetry> convention gives $s\Psi=hF+\xi h^2/2-\bar c(\Box+2A\cdot\partial)c$. The auxiliary-field integral at $\xi=0$ imposes the exact condition; finite $\xi$ gives a weighted gauge condition. This real functional is distinct from a <complex quadratic Abelian gauge condition>.
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