  The aim of this work is to apply the observable-state model for the quantum
field theory of a \phi^n self- interaction. We show how to obtain finite values
for the 2-point and n-point correlation functions without introducing
counterterms in the Lagrangian. Also, we show how to obtain the renormalization
group equation for the mass and the coupling constant. Finally, we found the
dependence of the coupling constant with the energy scale and we discuss the
validity of the observable-state model in terms of the projection procedure.
