Two- and Three-particle States in a Nonrelativistic Four-fermion Model in the Fine-tuning Renormalization Scheme. Goldstone mode "against" extension theory

Physics – High Energy Physics – High Energy Physics - Theory

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23 pages, LaTeX, changed content, added references and two figures, to appear in the Few Body Systems

Scientific paper

10.1007/s006010170010

In a nonrelativistic contact four-fermion model we show that simple regularisation prescriptions together with a definite fine-tuning of the cut-off-parameter dependence of ``bare'' quantities give the exact solutions for the two-particle sector and Goldstone modes. Their correspondence with the self-adjoint extension into Pontryagin space is established leading to self-adjoint semi-bounded Hamiltonians in three-particle sectors as well. Renormalized Faddeev equations for the bound states with Fredholm properties are obtained and analysed.

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