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

Role of cytokine and Toll-like receptor genes in pathogenesis of inborn heart disease

Sporadic congenital heart disease (CHD) may result from immune disorders in the mother – embryo system and/or constitutional disorders in regulatory systems, including those associated with TLR receptors, cytokines and their receptors. The aim of our study was to investigate associations between cytokine and TLR genes and sporadic congenital heart disease in children. In the main group, 188 children with sporadic (without family history) congenital heart defects were examined. Separate groups of CHD were identified: septal CHD – 98 children; valvular heart disease – 17 children; Fallot tetralogy – 15 children; aorta coarctation – 10 children; fetal drains – 32 children; single ventricle affection – 9 children, and anomalous drainage of v. pulmonalis was diagnosed in 7 children. The control group included 103 age- and sex-matched healthy children. We have determined gene polymorphisms of five genes encoding cytokines and their receptors (IL6 rs1800796, IL6 rs2069827, IL6R rs2228145, IL6R rs2229238, IL8 rs4073, IL10 rs1800871, IL10 rs1800896, IL10 rs1800872, TNF rs1800629, TNF rs361525, TNF rs1799964), four genes Toll-like receptors (TLR: TLR1 rs5743611, TLR1 rs5743551, TLR2 rs5743708, TLR2 rs3804099, TLR4 rs4986791, TLR4 rs4986790, TLR6 rs3775073, TLR6 rs5743810). The dbSNP, SNPinfo, SNPnexus databases were used to select and design test systems. Stepwise logistic regression was the main method of statistical analysis. Clinical diagnosis of congenital heart defects is associated with immune regulatory genes. In particular, the missense mutation TLR6 rs5743810, which was a predictor of congenital valvular heart disease, is of particular importance. Development of congenital heart valve defects and aortic coarctation is associated with intergenic interactions of TLR2 rs5743708 with TLR6 rs5743810, and TLR2 rs5743708 with TLR6 rs3775073, respectively. For congenital heart valve defects, such polymorphic regions are as follows: IL6 rs2069827, IL6R rs2229238, and IL8 rs4073, for aortic coarctation – IL6R rs2228145, IL8 rs4073. Development of septal congenital heart defects is associated with general contribution of polymorphic variants of the TLR genes and cytokines to this pathology. A missense mutation of the TLR4 rs4986790 gene and a TNF rs1799964 mutation leading to increased synthesis of the TNFα molecule, may have a combined effect on this process. In general, contribution of TLR and cytokine genes interactions to the CHD development seems to be not significant