28 research outputs found
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
One-particle excitations and bound states in non-relativistic current x current model
Vacuum structure, one-particle excitations' spectra and bound states of these excitations are studied in frame of non-relativistic quantum field model with current \times current type interaction. Hidden symmetry of the model is found. It could be broken or exact depending on the coupling constant value. The effect of "piercing" vacuum , generating the appearance of heavy fermionic excitations, could occur in the spontaneously broken phase
Fine-Tuning Renormalization and Two-particle States in Nonrelativistic Four-fermion Model
Various exact solutions of two-particle eigenvalue problems for
nonrelativistic contact four-fermion current-current interaction are obtained.
Specifics of Goldstone mode is investigated. The connection between a
renormalization procedure and construction of self-adjoint extensions is
revealed.Comment: 13 pages, LaTex, no figures, to be published in IJMP
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