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

Write the gauge-fixing and ghost action as the BRST transformation of the gauge-fixing fermion:with harmless rescalings of $B$ accommodating the convention $s{\bar{c}}^a=\xi B^a$ used in the question. The gauge-invariant action obeys $sS[A]=0$, while nilpotence givesThus the entire gauge-fixed action is BRST invariant. Eliminating the auxiliary field $B^a$ by its algebraic field equation reproduces the axial gauge-fixing term and the ghost action found in part (b).

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