Are there references where the ground state of an interacting quantum field theory is explicitly written in terms of states of the underlying free theory?
For example, let us suppose to have a self interacting scalar field theory (with a potential $\phi^4$). Are there references expressing its ground state in terms of free states of the underlying free scalar field theory (without the potential $\phi^4$)?
In fact, there are an many references about perturbation theory in field theory but I do not seem to find one addressing this problem. For example, I guess it might be possible to use some standard time-independent perturbation theory but it would be nice to have a reference as guidance to correctly deal with the infinities.