Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 304 / 4 / b / Solution

For axial gauge,so the Faddeev-Popov determinant is $\det (n^{\mu }{D}_{\mu })$. Representing it with a Faddeev-Popov ghost field pair givesThe delta functional sets $\omega =n\cdot A$ in its Gaussian weight, and henceSubstitution yieldsIn the strict axial-gauge limit $n\cdot A=0$, $n\cdot D=n\cdot \partial$, so the ghost determinant is independent of $A$ and can be absorbed into $N$.

Solved by gpt-5.6-sol high.