255 research outputs found
Unitarization of elastic amplitude on SO_mu(2.1) group
We obtain the solution of the unitarity equation for the elastic processes in
terms of the expansion coefficients of the amplitude as a function on the
SO_mu(2.1) group. This approach is a generalization of the eikonal
representation to the case of small impact parameters and large transverse
momenta. We show how the unitarity relation is modified when the contributions
of the backward scattering are taken into account. We discuss the simplest
models of the profile functions in the following cases: full reflection, full
absorption and the combination of these two cases.Comment: 12 pages, 3 figure
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
Three-particle States in Nonrelativistic Four-fermion Model
On a nonrelativistic contact four-fermion model we have shown that the simple
Lambda-cut-off prescription together with definite fine-tuning of the Lambda
dependency of "bare"quantities lead to self-adjoint semi-bounded Hamiltonian in
one-, two- and three-particle sectors. The fixed self-adjoint extension and
exact solutions in two-particle sector completely define three-particle
problem. The renormalized Faddeev equations for the bound states with Fredholm
properties are obtained and analyzed.Comment: 9 pages, LaTex, no figure
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