  The purpose of this work is to rewrite the generating functional of phi^4
theory for the n = 0 and n = 4 correlation functions as the inner product of a
state with an observable, as we did in [J. S. Ardenghi, M. Castagnino, Phys.
Rev. D, 85, 025002, (2012)] for the two-points correlation function. The
observables are defined through the external sources and the states are defined
through the correlation function itself. In this sense, the divergences of
Quantum Field Theory (QFT) appear in the reduced state by taking the partial
trace of the state with respect to the internal vertices that appear in the
perturbation expansion. From this viewpoint, the renormalization can be
substituted by applying a projector on the internal quantum state. The
advantage of this new insight is that we can obtain finite contributions of the
correlation functions without introducing counterterms in the Lagrangian or by
manipulating complex divergent quantities.
