Disappearance of Schwinger's string at the charge - monopole "molecule"

An equivalence of total momentum operator of charge - monopole system to the momentum operator of a symmetrical quantum top is observed. This explicitly shows the string independence of Dirac's quantization condition leading to disappearance of Schwinger's string and reveals some properties of diatomic molecule for this system.Comment: 9 page

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

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.Comment: 23 pages, LaTeX, changed content, added references and two figures, to appear in the Few Body System