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

For a gauge orbit near a root ${\alpha }_0$ of $G(A^{\alpha })=0$, functional linearization givesThe multidimensional delta-function change-of-variables formula therefore givesComparison with the defining identity provesup to the usual field-independent normalization and a choice of determinant sign on the gauge patch.

Solved by gpt-5.6-sol high.