The physical interpretation of these new operators is that of so-called quasiparticle states. This means that a state defined by the addition of one extra particle to a reference state \( |c\rangle \) may not necesseraly be interpreted as one particle coupled to a core. We define now new creation operators that act on a state \( \alpha \) creating a new quasiparticle state $$ \begin{equation} b_\alpha^\dagger|c\rangle = \Bigg\{ \begin{array}{ll} a_\alpha^\dagger |c\rangle = |\alpha\rangle, & \alpha > F \\ \\ a_\alpha |c\rangle = |\alpha^{-1}\rangle, & \alpha \leq F \end{array} \tag{70} \end{equation} $$ where \( F \) is the Fermi level representing the last occupied single-particle orbit of the new reference state \( |c\rangle \).

The annihilation is the hermitian conjugate of the creation operator $$ b_\alpha = (b_\alpha^\dagger)^\dagger, $$ resulting in $$ \begin{equation} b_\alpha^\dagger = \Bigg\{ \begin{array}{ll} a_\alpha^\dagger & \alpha > F \\ \\ a_\alpha & \alpha \leq F \end{array} \qquad b_\alpha = \Bigg\{ \begin{array}{ll} a_\alpha & \alpha > F \\ \\ a_\alpha^\dagger & \alpha \leq F \end{array} \tag{71} \end{equation} $$