If one assumes that energy levels are never half filled (always occupied by either 0 or 2 fermions), then the pairing model is equivalent to a system of N pairs of fermions that occupy P doubly-degenerate energy levels \begin{align} H = 2\sum_{p} \delta_pA_p^{\dagger}A_p+\sum_{pq}g_{pq}A_p^{\dagger}A_q, \tag{20} \end{align} where p and q sum from over the set \{1,...,p\} and \begin{align*} A_p &= a_{p-}a_{p+} \\ A^{\dagger}_p &= a^{\dagger}_{p+}a^{\dagger}_{p-}, \end{align*} are the fermionic pair creation and annihilation operators.