Axial gauge

An axial gauge imposes $n^{\mu }{A}_{\mu }=0$ for a fixed vector $n^{\mu }$. Its Faddeev-Popov operator is $n^{\mu }{D}_{\mu }$; on the strict gauge slice its gauge-field-dependent part vanishes, so its ghosts decouple.

The inverse of $n\cdot \partial$ and the axial-gauge propagator are singular when $n\cdot k=0$. A pole prescription and residual-gauge boundary conditions specify these inverses. They must be compatible throughout a calculation; formal ghost decoupling alone does not specify them.

In strict axial gauge, the gauge-boson propagator obeys $n^{\mu }{D}_{\mu \nu }(k)=0$ and contains poles at $n\cdot k=0$. Its contraction with conserved external currents removes the gauge-choice terms. Consistent calculations require an axial-gauge pole prescription.