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V. M. Leviant

Publications and source records attributed to V. M. Leviant.

7 recordsLinked to original sources
arXiv2000

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.

hep-th↗
arXiv1997

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.

hep-th↗
arXiv1996

Dynamical mapping method in nonrelativistic models of quantum field theory

The solutions of Heisenberg equations and two-particles eigenvalue problems for nonrelativistic models of current-current fermion interaction and $N, Θ$ model are obtained in the frameworks of dynamical mapping method. The equivalence of different types of dynamical mapping is shown. The connection between renormalization procedure and theory of selfadjoint extensions is elucidated.

hep-th↗
arXiv1995

One-particle excitations and bound states in non-relativistic current $\times$ 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.

quant-ph↗
arXiv1994

Analysis of one particle excitations in phenomenological models of QCD

In these notes for the quark Nambu-Jona-Lasinio model and for the phenomenological four fermionic model of QCD we analyze vacuum energy structure and calculate dependence of energy of one-particle excitations on momentum. We reveal existence of two different types of excitations above the vacuum with the respective minimization of the vacuum energy density. First type of excitation energy spectrum is the usual spectrum of relativistic massive particle, but the second one has a linear dependence on momentum.

hep-ph↗
arXiv1994

Solution of The Heisenberg Equation For The Four-fermion Contact Interaction by The Method of Dynamical Mappings

In the paper we consider non-relativistic analog of the Nambu-Jona-Lasinio model and demonstrate, by this most simplified example, the method of dynamical mappings of Heisenberg fields on "physical" fields. We obtain the expressions for one particle eigen-excitation spectrum of full Hamiltonian (spectrum of "clad" fermions), wave function of two excitations' bound state and its mass, and compute the Bethe-Solpither amplitude. We derive as well the relation for the density of vacuum energy as a function of mapping parameters. The minimization of energy leads us to the fixation of these parameters. The method admits the generalization on the relativistic case.

hep-ph↗