Related papers: Abnormal solutions of Bethe--Salpeter equation wit…
In the Wick-Cutkosky model, where two scalar massive constituents interact by means of the exchange of a scalar massless particle, the Bethe-Salpeter equation has solutions of two types, called "normal" and "abnormal". In the…
The Bethe-Salpeter equation for two massive scalar particles interacting by scalar massless exchange has solutions of two types, which differ from each other by their behavior in the non-relativistic limit: the normal solutions which turn…
Bethe-Salpeter equation, for massless exchange and large fine structure constant $\alpha>\pi/4$, in addition to the Balmer series, provides another (abnormal) series of energy levels which are not given by the Schr\"odinger equation. So…
The Bethe-Salpeter equation for system of two oppositely charged particles not only reproduces the Coulomb spectrum, but, for enough large coupling constant ${\cal C}>\frac{\pi}{4}$, predicts additional levels not predicted by the…
Homogeneous Bethe-Salpeter equation for simplest Wick-Cutkosky model is studied in the case when the mass of the two-body system is more then the sum of constituent particles masses. It is shown that there is always a small attraction…
It is taken for granted that bound systems are made of massive constituents that interact through particle exchanges (charged particles interacting via photon exchanges, quarks in elementary particles interacting via gluon exchanges, and…
As well known, the spectrum of a non-relativistic two-body system interacting by the Coulomb potential is the Balmer series $E_n=\frac{\alpha^2m}{4n^2}$ produced by the Schr\"odinger equation. In 1954, Wick and Cutkosky have found, in the…
In order to solve the Bethe-Salpeter equation (BSE) in the Minkowski space, we first introduce the Nakanishi integral representations of the Bethe-Salpeter amplitude (BSA) and the Bethe-Salpeter wave function (BSWF). We then derive the…
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…
The Bethe-Salpeter Equation for a two-scalar, S-wave bound system, interacting through a massive scalar, is investigated within the ladder approximation. By assuming a Nakanishi integral representation of the Bethe-Salpeter amplitude, one…
The ladder Bethe-Salpeter Equation of a bound (1/2)+ system, composed by a fermion and a scalar boson, is solved in Minkowski space, for the first time. The formal tools are the same already successfully adopted for two-scalar and…
It is shown that there exist solutions of the quasipotential equations exhibiting the abnormal type behaviour of the Bethe-Salpeter equation.
The problem of calculating of the mass spectrum of the two-body Bethe-Salpeter equation is studied with no reduction to the three-dimensional ("quasipotential") equation. The method to find the ground state and excited states for a channel…
We develop a new method of solving Bethe-Salpeter (BS) equation in Minkowski space. It is based on projecting the BS equation on the light-front (LF) plane and on the Nakanishi integral representation of the BS amplitude. This method is…
We use the worldline representation of field theory together with a variational approximation to determine the lowest bound state in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons.…
The contribution to the binding energy of a two-body system due to the crossed two-boson exchange contribution is calculated, using the Bethe-Salpeter equation. This is done for distinguishable, scalar particles interacting via the exchange…
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…
The Bethe-Salpeter (BS) equation in the ladder approximation is studied within a scalar theory: two scalar fields (constituents) with mass $m$ interacting via an exchange of a scalar field (tieon) with mass $\mu$. The BS equation is written…
The Bethe-Salpeter equation provides the most widely used technique to extract bound states and resonances in a relativistic Quantum Field Theory. Nevertheless a thorough discussion how to identify its solutions with physical states is…
By application of the 'geometric spectral inversion' technique, which we have recently generalized to accommodate also singular interaction potentials, we construct from spectral data emerging from the solution of the Minkowski-space…