arXiv subjects
Publications and source records attributed to A. V. Sinitskaya.
The pre-asymptotic analysis of the multichannel scattering problem for particles with an arbitrary spin and short-range interactions has been presented. The complete operator-valued dependence of the scattered differential flux on the distance to the target exactly consistent with the unitarity condition has been obtained.
In this paper, we will analyze the short distance corrections to low energy scattering. They are produced because of an intrinsic extended structure of the background geometry of spacetime. It will be observed that the deformation produced by a minimal measurable length can have low energy consequences, if this extended structure occurs at a scale much larger than the Planck scale. We explicitly calculate short distance corrections to the Green function of the deformed Lippmann-Schwinger equation, and to the conserved currents for these processes. We then use them to analyze the pre-asymptotic corrections to the differential scattering flux at finite macroscopically small distances.
In a wide class of potentials the exact asymptotic dependence on finite distance R from scattering center is established for outgoing differential flux. It is shown how this dependence is eliminated by integration over solid angle for total flux, unitarity relation, and optical theorem. Thus, their applicability domain extends naturally to the finite R.
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.
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.
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.
The bound states of two particles are studied in frames of non-relativistic quantum field model with current $\times$ current type interaction by analyzing the Bethe-Salpeter amplitudes. The Bethe-Salpeter equations are obtained in closed form. The existence of Goldstone mode corresponding to the spontaneous breaking of additional SU(2) symmetry of the model is revealed.
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.
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.
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.