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

Computational modeling of an economy using elements of artificial intelligence

The goal of this dissertation was to develop tools for analyzing economic performance while agents were constrained to be constructively rational. To achieve this goal, firstly, tools for introducing forward-looking agents into agent-based frameworks were developed. These agents were shown to be a feasible alternative to the assumption of rational expectations, albeit with some limitations, as could be expected from any computational method. Several testing frameworks were also developed. Smaller ones were used to explore economic effects of decision procedures used by agents on macro- and micro-levels. A more advanced framework was formulated to facilitate the analysis of the interactions between institutional structures and macroeconomic policies. These frameworks were shown to be scalable and useful tools for the analysis of both micro-level decisions of agents and macroeconomic policies of central banks

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

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