= Cooper-pair pseudospin coherent state
{c}
The empty and doubly occupied states of a paired <momentum> block form a two-level space. Define $S_k^+=a_{k\uparrow}^\dagger a_{-k\downarrow}^\dagger$, $S_k^-=a_{-k\downarrow}a_{k\uparrow}$ and $S_k^z=(n_{k\uparrow}+n_{-k\downarrow}-1)/2$. They obey the spin algebra on that space. The normalized factor $u_k|0\rangle+v_k|\mathrm{pair}\rangle$ is a spin-one-half coherent state; the product over blocks is the <BCS ground state>. Pauli exclusion prevents interpreting a block as an unrestricted harmonic-oscillator pair mode.
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