In section 6.1, eqs(6.4) and eq(6.5), the $|i\rangle$ and $|f\rangle$ are defined as $$|i\rangle=\sqrt{2\omega_1}\sqrt{2\omega_2} a_{p_1}^{\dagger}(-\infty)a_{p_2}^{\dagger}(-\infty)|\Omega\rangle,\tag{6.4}$$ $$|f\rangle=\sqrt{2\omega_3}...\sqrt{2\omega_n}a_{p_3}^{\dagger}(\infty)...a_{p_n}^{\dagger}(\infty)|\Omega \rangle.\tag{6.5}$$
In the next, eq(6.6), the books says the $S$-Matrix is defined as $$\langle f|S|i\rangle=2^{n/2}\sqrt{\omega_1...\omega_n}\langle\Omega|a_{p_3}(\infty)...a_{p_n}(\infty)a_{p_1}^{\dagger}(-\infty)a_{p_2}^{\dagger}(-\infty)|\Omega \rangle .\tag{6.6}$$
But by the definitions, the righthand-side is nothing but $\langle f|i\rangle $, so we get $$ \langle f|S|i\rangle=\langle f|i\rangle~?$$ I think this is wrong. Or did I misunderstand something?
