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Could you please elaborate more or provide the full working? I have tried doing the complete derivation but I do not quite get it. It would be very helpful @user200143
$l$ here is large, as I mentioned in my question, I am trying to compute de CMB power spectrum for which I consider a range of $l$ in between 2 and 1500 @ZeroTheHero
Thank you very much for your comments. This mathematica notebook is from Daniel Baumann and it is the one that he suggests as simple exercise in equation 3.3.70lecture notes Baumann.@EmilioPisanty
Taking $\psi=a+b^{\dagger}$, we would get $\psi^{\dagger} \psi$ contains a term like $bb^{\dagger} $, which isn't normal ordered, so I actually get that either order are not normal ordered. Also about your earlier explanation, since we have multiple $\psi$ terms wouldn´t the $b$´s contained in them contribute via the other $b^{\dagger}$´s in $\psi^{\dagger}$? @Hosein
