Let $\phi$ be a scalar field and then I see the following expression for the square of the normal ordered version of $\phi^2(x)$.
$T(:\phi^2(x)::\phi^2(0):) = 2<0|T(\phi(x)\phi(0))|0>^2 + 4<0|T(\phi(x)\phi(0))|0>:\phi(x)\phi(0): + :\phi^2(x)\phi^2(0):$
It would be great if someone can help derive the above expression - may be from scratch - and without outsourcing to Wick's theorem - and may be help connect as to why the above is related (equal?) to the Wick's theorem?
Isn't the above also known as OPE (Operator Product Exapnsion)? If yes, then is there at all any difference between OPE and Wick's theorem? Is there a systematic way to derive such OPEs?
Can one help extend this to Fermions?