 Scalar-dependent gauge fixing

Scalar-dependent gauge fixing chooses a gauge condition containing both a gauge field and a scalar field. After spontaneous symmetry breaking, expanding a scalar kinetic term often produces mixing between the vector field and a scalar phase fluctuation. A suitable gauge condition can cancel that mixing in the quadratic action.

For example, a condition schematically $G=\partial \cdot A-\xi m\chi$ leads to a gauge fixing term $-G^2/(2\xi )$, with the sign chosen consistently with the original mixing. The Faddeev-Popov operator follows by varying the full $G$, including its scalar dependence. Thus ghosts can acquire scalar-dependent interactions even for an Abelian theory when the gauge condition is nonlinear. Cancelling the quadratic mixing does not imply that all vector–scalar interactions disappear, or that physical predictions can depend on the gauge-fixing parameter.