The bound state problem for a gauge invariant quark-antiquark system is considered in the instantaneous rest frame. Focus here is on the long range non-perturbative interaction. A two-time Green’s function is constructed for Salpeter amplitudes. The corresponding Schrödinger equation is found to be in the Salpeter form with a Wilson-loop term as the instantaneous kernel.

The proper support of generalized parton distributions from relativistic constituent quark models with pointlike constituents is studied. The correct support is guaranteed when the vertex function does not depend on the relative momentum. We show that including quark interactions in models with pointlike constituent quarks might lead to a support problem.

The e-e bound state spectrum of three-dimensional QED is investigated in the quenched ladder approximation to the homogeneous Bethe-Salpeter equation with fermion propagators from a rainbow approximation Schwinger-Dyson solution with a variable fermion mass. A detailed analysis of the analytic structure of the fermion propagator is performed so as to test the appropriateness of the methods empl...

Abstract The quark dynamics inside light mesons, except pseudoscalar ones, can be quite well described by a spinless Salpeter equation supplemented by a Cornell interaction (possibly partly vector, partly scalar). A mass formula for these mesons can then be obtained by computing analytical approximations of the eigenvalues of the equation. We show that such a formula can be derived by combining...

In a previous letter, we computed the decay constants of heavy pseudoscalar mesons in the framework of relativistic (instantaneous) Bethe-Salpeter method (full 0− Salpeter equation), in this letter, we solve the full 1− Salpeter equation and compute the leptonic decay constants of heavy-heavy and heavy-light vector mesons. The theoretical estimate of mass spectra of these heavy-heavy and heavy-...