 Unitary flavour symmetry of degenerate Dirac fields

For $N$ Dirac fields with common mass, $\mathcal{L}=\bar{\Psi }(i/\partial -m{1}_N)\Psi$ is invariant under constant complex-linear rotations $\Psi \mapsto U\Psi$ with $U\in U(N)$. A Hermitian flavour generator $T^A$ has Noether current $j_A^{\mu }=\bar{\Psi }{\gamma }^{\mu }{T}^A\Psi$. A nondegenerate fermion mass matrix restricts the symmetry to unitary matrices commuting with it. If the theory is entirely free and rotations into charge-conjugate fields are allowed, its enhanced internal symmetry of free Dirac fields can be larger than this subgroup.