Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 305 / 3 / i / Solution

The axial $U(1)$ is anomalous, while vector fermion number survives. In a left-handed convention, put ${\tilde{\psi }}_R=({\psi }_R{)}^c$. The continuous quantum symmetry and charges areup to finite quotients and the surviving discrete axial symmetry.