Exact solution for the order parameter profiles and the Casimir force in $^4$He superfluid films in an effective field theory

We present an analytical solution of an effective field theory which, in one of its formulations, is equivalent to the Ginzburgs $Psi$-theory for the behavior of the Casimir force in a film of $^4$He in equilibrium with its vapor near the superfluid transition point. We consider thr