= Complex quadratic Abelian gauge condition
{title2=$F[A]=\partial_\mu A_\mu+iA_\mu A_\mu$}
The formal variation of this condition is $\delta F=(\partial^2+2iA\cdot\partial)\alpha$. Thus its <Faddeev-Popov ghost field> operator can be chosen as $\mathcal O_A=-\partial^2-2iA\cdot\partial$. With $D_\mu=\partial_\mu+iA_\mu$, one has $D^2=\partial^2+2iA\cdot\partial+iF[A]$, so $\mathcal O_A=-D^2$ on the formal gauge slice. The <reality obstruction for a complex Euclidean gauge condition> prevents interpreting this slice as an ordinary real Euclidean <gauge fixing> without an additional complex-contour prescription.
Back to article page
