= Solution
{c}
Collect the two <Dirac fields> into $\Psi=(\psi_1,\psi_2)^T$, with a common nonzero <mass> $m$. Then
$$
\boxed{\mathcal L=\sum_{i=1}^2\bar\psi_i(i\not\partial-m)\psi_i
=\bar\Psi(i\not\partial-m\mathbf1_2)\Psi.}
$$
Among complex-linear rotations of the <Dirac fields>, the <internal symmetry of a classical field theory> is $\Psi\mapsto U\Psi$, $U\in U(2)$, with $\bar\Psi\mapsto\bar\Psi U^\dagger$. Unitarity preserves the kinetic term, and the <mass matrix> commutes with every $U$. This <unitary flavour symmetry of degenerate Dirac fields> has <group> $(SU(2)\times U(1))/\mathbb Z_2$, where the quotient avoids counting the common central element twice.
Choose the four <Hermitian matrices> $T^0=\mathbf1_2/2$, $T^a=\sigma^a/2$ for $a=1,2,3$, with $\sigma^a$ the <Pauli matrices>. Promoting the four parameters to functions gives $\delta S=-\int d^4x\,(\partial_\mu\alpha^A)\bar\Psi\gamma^\mu T^A\Psi$. The four <Noether currents> are therefore
$$
\boxed{j_A^\mu=\bar\Psi\gamma^\mu T^A\Psi,\qquad A=0,1,2,3.}
$$
Their divergences vanish by the equal-mass <Dirac equations>. The singlet is half the total <Dirac current>; the other three currents rotate the two species.
\b[Free-theory qualification.] If “global internal symmetry” allows mixing the <Dirac fields> with <charge-conjugate fields>, the completely free theory written here has a larger <enhanced internal symmetry of free Dirac fields>. Write $\psi_i=(\lambda_{2i-1}+i\lambda_{2i})/\sqrt2$ using four <Majorana fermions>. Up to a <total derivative>,
$$
\mathcal L=\frac12\sum_{A=1}^4\bar\lambda_A(i\not\partial-m)\lambda_A.
$$
The full <orthogonal group> $O(4)$ acts on the four real species; its connected part is $SO(4)$. Its six <Noether currents> can be chosen as $J_{AB}^\mu=i\bar\lambda_A\gamma^\mu\lambda_B$ for $A<B$, up to the common sign convention. The antisymmetry of this <Majorana fermion> vector bilinear makes these the six independent rotations. A concrete rotation outside the stated complex-linear $U(2)$ is $\lambda_2\mapsto\cos\theta\lambda_2+\sin\theta\lambda_3$, $\lambda_3\mapsto-\sin\theta\lambda_2+\cos\theta\lambda_3$: it preserves the displayed <Lagrangian density> while mixing $\psi_i$ with their <charge-conjugate fields>. The usual $U(2)$ answer specifies the subgroup preserving the chosen common <fermion number>.
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