Say we have an expression of the form: $$ \left<0\right|:\phi(x)^2: : \phi(y)^2:\left|0\right>, $$ where $\phi$ is some scalar field. I have heard the claim several times, that in evaluating this expression using Wick contractions, one only has to contract terms between groups of normal ordered terms. In this example this would mean we only have to contract $\phi(x)$ with $\phi(y)$ but not $\phi(x)$ with $\phi(x)$. I have no clue how to derive this. Has anyone got an idea?
EDIT: And say we consider anticommuting operators, would we have: $$ \left<:\Psi^{\dagger}(x)\Psi(x)::\Psi^{\dagger}(0)\Psi(0):\right> = (-1)^3\left<\Psi^{\dagger}(x)\Psi(0)\right>\left<\Psi^{\dagger}(x)\Psi(0)\right>, $$ or with a plus sign?
