Two fermion relativistic bound states

We consider the relativistic quantum mechanics of a two interacting fermions system. We first present a covariant formulation of the kinematics of the problem and give a short outline of the classical results. We then quantize the system with a general interaction potential and deduce the explicit equations in a spherical basis. The case of the Coulomb interaction is studied in detail by numerical methods, solving the eigenvalue problem for J=0, J=1, J=2 and determining the spectral curves for a varying ratio of the mass of the interacting particles. Details of the computations, together with a perturbative approach in the mass ratio and an extended description of the ground states of the Para- and Orthopositronium are given in Appendix.Comment: 26 pages, 6 figure

Relativistic two-body calculation of bbˉb\bar{b}-mesons radiative decays

This paper is a prosecution of a previous work where we presented a unified two-fermion covariant scheme which produced very precise results for the masses of light and heavy mesons. We extend the analysis to some radiative decays of mesons $\Upsilon,\,\chi_{b2}\,,h_b\,,\chi_{b1}\,,\chi_{b0}\,,\eta_b\,$ and we calculate their branching ratios and their widths. For most of them we can make a comparison with experimental data finding a good agreement.For the decays for which data are not available we compare ours with other recent theoretical previsions.Comment: 7 pages, 1 figur

Exponential mapping for non semisimple quantum groups

The concept of universal T matrix, recently introduced by Fronsdal and Galindo in the framework of quantum groups, is here discussed as a generalization of the exponential mapping. New examples related to inhomogeneous quantum groups of physical interest are developed, the duality calculations are explicitly presented and it is found that in some cases the universal T matrix, like for Lie groups, is expressed in terms of usual exponential series.Comment: 12 page

Stiffening effects-controlling sizing procedure of ADAS dampers in seismic retrofit of frame structures

Added Damping and Stiffness (ADAS) steel dissipators are among the most classical devices installed in dissipative bracing systems for the advanced seismic retrofit of frame buildings. An energy-based sizing procedure is formulated in this study for this class of dampers, where the total number of constituting plates is directly related, without iterative steps, to the supplementary damping energy required to jointly reduce stress states in structural members and storey drifts. The stiffening effects of the dissipative braces are expressly controlled, so as to compensate for the increase in storey shears induced by their incorporation in the frame skeleton. The sizing procedure is demonstratively applied to the retrofit design of a 6-storey reinforced concrete building, to explicate and discuss the use of its analytical relations and relevant limitations in practice. The evaluation of the seismic performance of the structure in retrofitted conditions allows comparing the response of the dissipative bracing system with the hypotheses formulated at the sizing stage