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In a nonrelativistic contact four-fermion model we show that simpleregularisation prescriptions together with a definite fine-tuning of thecut-off-parameter dependence of ``bare'' quantities give the exact solutionsfor the two-particle sector and Goldstone modes. Their correspondence with theself-adjoint extension into Pontryagin space is established leading toself-adjoint semi-bounded Hamiltonians in three-particle sectors as well.Renormalized Faddeev equations for the bound states with Fredholm propertiesare obtained and analysed.Comment: 23 pages, LaTeX, changed content, added references and two figures,  to appear in the Few Body System

few-body systems

Two- and Three-Particle States in a Nonrelativistic Four-Fermion Model in the Fine-Tuning Renormalization Scheme: Goldstone Mode Versus Extension Theory