Kulikov D. Relativistic oscillator models with non-minimally introduced interaction

The objects are the features of the bound-state spectra of relativistic particles in potential fields and of two-body systems. The goal is the construction of the relativistic quantum-mechanical oscillator models with the potential interaction introduced in minimal and non-minimal ways, the analysis of the properties of the bound-state spectra of the constructed models and the verification of their applicability in hadron physics. Research techniques: methods of the theory of differential equations, the theory of functions of a complex variable, and the group theory; methods of asymptotical expansions. New exactly solvable oscillator models with non-minimally introduced interaction are found and analyzed, namely, an alternative model of the Duffin-Kemmer-Petiau oscillator and the one for the fermion-boson oscillator which additionally includes the interaction introduced in the minimal way. For the Klein-Gordon and Duffin-Kemmer-Petiau equations with the non-minimally introduced interaction and spherically symmetric Lorentz-scalar and Lorentz-vector potentials of an arbitrary form the recursion scheme for calculating the bound-state Regge trajectories is elaborated. Based on the extension of the SL(2,C) group, the new relativistic quantum-mechanical equation for a fermion-boson system is constructed. Contrary to the standard ones, this equation includes the Lorentz-tensor potentials that describe the contribution of the fermion anomalous magnetic moment. The efficiency of the proposed models is confirmed by their application to the description of quarkonia and pionic hydrogen. Application area of the results is the investigation of the bound states in hadron physics and nuclear physics.