Renormalization of the coupled cluster equations in three-dimensionalφ4quantum field theory

We construct eigenstates of the (${\phi }^4$ ${)}_3$ quantum field theory in the framework of the coupled cluster method (CCM). Therefore the principle of coherence is stressed leading to a description of these states by an infinite set of correlation amplitudes. In the standard form of the CCM the amplitudes obey a hierarchy of coupled nonlinear integral equations containing some poorly defined terms because of ultraviolet divergences. We remove these divergences by a systematic transformation to an equivalent set of amplitudes. No expansion in the coupling constant is therefore required to make the hierarchy well defined. It is possible to find truncation schemes for the transformed amplitudes which are compatible with the requirement of renormalizability. We conclude that the CCM is helpful to analyze the structure of the vacuum and to make precise statements about the mass spectrum of superrenormalizable quantum field theories.