Related papers: 3D reduction of the three-fermion Bethe-Salpeter e…
We write a 3D equation for three fermions by combining the three two-body potentials obtained by the reductions of the corresponding two-fermion Bethe-Salpeter equations to equivalent 3D equations, putting the spectator fermion on the mass…
We write a 3D equation for three fermions by combining the three two-body potentials obtained in 3D reductions (based on a series expansion around a relative-energy fixing "approximation" of the free propagators) of the corresponding…
We perform a 3D reduction of the two-fermion Bethe-Salpeter equation based on Sazdjian's explicitly covariant propagator, combined with a covariant substitute of the projector on the positive-energy free states. We use this combination in…
We perform a 3D reduction of the two-fermion Bethe-Salpeter equation, by series expansion around a positive-energy instantaneous approximation of the Bethe-Salpeter kernel, followed by another series expansion at the 3D level in order to…
We compare two opposite ways of performing a 3D reduction of the two-fermion Bethe-Salpeter equation beyond the instantaneous approximation and Salpeter's equation. The more usual method consists in performing an expansion around an…
Starting with the homogeneous Bethe-Salpeter equation for two fermions, we perform a 3D reduction using a series expansion around an unspecified positive-energy instantaneous approximation of the kernel. A second series expansion is made,…
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…
A three-dimensional reduction of the homogeneous Bethe-Salpeter equation retaining, in contrast to the Salpeter equation, the exact propagators (crucial for, e.g., a proper incorporation of dynamical chiral symmetry breakdown) is proposed.…
Five different versions of the three-dimensional (3D) reduction of the Bethe-Salpeter (BS) equation in the instantaneous approximation for kernel of BS equation for the two-fermion systems are formulated. The normalization condition for the…
To understand the mechanism of the fermion pair and fermion-antifermion pair condensation,the solutions of Bethe-Salpeter equation in QED$_{3}$ is examined.In the ladder appoximation our solution for the axial-scalar is consistent with…
We show that the 3D reductions of the Bethe-Salpeter equation have the same bound state spectrum as the original equation, with the possible exception of some solutions for which the corresponding 3D wave function vanishes. The abnormal…
This is the first of a series of three papers treating light baryon resonances (up to 3 GeV) within a relativistically covariant quark model based on the three-fermion Bethe-Salpeter equation with instantaneous two- and three-body forces.…
We apply the 3D reduction method we recently proposed for the N-particle Bethe-Salpeter equation to the 4-particle case. We find that the writing of the Bethe-Salpeter equation is not a straightforward task when N is larger or equal to 4,…
Bethe-Salpeter equation is solved for bound state composed of two fermions mediated by pion exchange force of the pseudovector coupling. Expanding the amplitude by gamma matrices the one-dimensional integral equation is derived. It…
We show the light-front representation of the field theoretical Bethe-Salpeter equation (BSE) in the ladder approximation using the quasi potential reduction. We discuss the equivalence of the covariant ladder Bethe-Salpeter equation with…
We investigate the relation between different three-dimensional reductions of the Bethe-Salpeter equation and the analytic structure of the resultant amplitudes in the energy plane. This correlation is studied for both the $\phi^2\sigma$…
We present an intuitive, light front reduction scheme for the Bethe-Salpeter equation that consists of iterations of the (light front) energy dependent covariant equation followed by an instantaneous approximation. This scheme is equivalent…
Actual solutions of the Bethe-Salpeter equation for a two-fermion bound system are becoming available directly in Minkowski space, by virtue of a novel technique, based on the so-called Nakanishi integral representation of the…
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…
A recent approach for constructing an exact 3D reduction of the 4D matrix elements of the electromagnetic current for an interacting two-fermion system, is briefly reviewed. The properties of the obtained 3D current, like the fulfillment of…