A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests tha...

The difficulties that typically prevent numerical solutions from being obtained to finite-energy, two-body, bound-state Bethe-Salpeter equations can often be overcome by expanding solutions in terms of basis functions that obey the boundary conditions. The method discussed here for solving the Bethe-Salpeter equation requires only that the equation can be Wick rotated and that the two angular v...

In the framework of ‘instantaneous approximations’ to the Bethe–Salpeter formalism for the description of bound states within quantum field theories, depending on the Lorentz structure of the Bethe–Salpeter interaction kernel solutions of the (full) Salpeter equation with some confining interactions may exhibit certain instabilities [1], possibly related to the Klein paradox, signalling the dec...

A three-dimensional reduction of the two-particle Bethe-Salpeter equation is proposed. The proposed reduction is in the framework of light-front dynamics. It yields auxiliary quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded according to the number of particles exchanged at a given light-front time. An example suggests tha...

applying the variational method, the spinless reduced bethe-salpeter (rbs) equation is solved for the mesonic systems, and the mass spectra are obtained. the method is applied to the hamiltonian with the gaussian and hydrogen-type trial wave functions, and different potential models are examined. the results for the different potentials are in challenge in light mesons, while they are consisten...

In quantum theory, the “spinless Salpeter equation,” the relativistic generalization of the nonrelativistic Schrödinger equation, is used to describe both bound states of scalar particles and the spin-averaged spectra of bound states of fermions. A numerical procedure solves the spinless Salpeter equation by approximating this eigenvalue equation by a matrix eigenvalue problem with explicitly k...

Consequent application of the instantaneous approximation to both the interaction and all propagators of the bound-state constituents allows us to forge, within the framework of the Bethe–Salpeter formalism for the description of bound states, an instantaneous form of the Bethe–Salpeter equation with exact (i.e., full) propagators of the bound-state constituents. This instantaneous equation gen...