The bound state Bethe-Salpeter amplitude was expressed by Nakanishi using a two-dimensional integral representation, in terms of a smooth weight function g, which carries the detailed dynamical information. A similar, but one-dimensional, integral representation can be obtained for the Light-Front wave function in terms of the same weight function g. By using the generalized Stieltjes transform...

The aim of this four-day workshop is to assess the present status, the latest achievements and future perspectives of first principles approaches to the study of spectroscopic properties of solids, nanostructures, systems with increasing complexity, and materials of technological and biological interest. More specifically, this workshop will offer the opportunity to take a look back on ten year...

The Bethe-Salpeter equation in non-commutative QED (NCQED) is considered for three-body bound state. We study the non-relativistic limit of this equation in the instantaneous approximation and derive the corresponding Schrödinger equation in non-commutative space. It is shown that the experimental data for Helium atom puts an upper bound on the magnitude of the parameter of non-commutativity, θ...

The Bethe-Salpeter equation in a strong magnetic field is studied for positronium atom in an ultra-relativistic regime, and a (hypercritical) value for the magnetic field is determined, which provides the full compensation of the positronium rest mass by the binding energy in the maximum symmetry state. The compensation becomes possible owing to the falling to the center phenomenon. The relativ...

Abstract. To study the characteristic features of relativistic bound systems, the Bethe-Salpeter equation (BSE) for two equal mass spin 1/2 particles (like the deuteron) is solved in the cm-frame for a covariant separable interaction kernel. For that purpose the BSE is transformed to an eigenvalue problem which is diagonalized numerically. The Bethe–Salpeter amplitudes (BSAs) are obtained strai...

A one parameter, model confined-gluon propagator is employed in a phenomenological application of the Dyson-Schwinger and Bethe-Salpeter equations to the calculation of a range of πand ρ-meson observables. Good agreement is obtained with the data. The calculated quark propagator does not have a singularity on the real-p2 axis. A mass formula for the pion, involving only the vacuum, dressed quar...

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and n...

Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three dimensional scattering integral equations satisfying constraints of relativistic unitarity and covariance, first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of va...

We adapt a general method to solve both the full and reduced Salpeter equations and systematically explore the conditions under which these two equations give equivalent results in meson dynamics. The effects of constituent mass, angular momentum state, type of interaction, and the nature of confinement are all considered in an effort to clearly delineate the range of validity of the reduced Sa...