We present a systematic algebraic and numerical investigation of the instantaneous Bethe-Salpeter equation. Emphasis is placed on confining interaction kernels of the Lorentz scalar, time component vector, and full vector types. We explore stability of the solutions and Regge behavior for each of these interactions, and conclude that only time component vector confinement leads to normal Regge ...

In this paper three types of relativistic bound-state equations for a fermion pair with instantaneous interaction are studied, viz., the instantaneous Bethe-Salpeter equation, the quasi-potential equation, and the two-particle Dirac equation. General forms for the equations describing bound states with arbitrary spin, parity, and charge parity are derived. For the special case of spinless state...

Several numerical investigations of the Salpeter equation with static confining interactions of Lorentz-scalar type revealed that its solutions are plagued by instabilities of presumably Klein-paradox nature. By proving rigorously that the energies of all predicted bound states are part of real, entirely discrete spectra bounded from below, these instabilities are shown, for confining interacti...

2014 A Bethe lattice with a given coordination number can be described in terms of a regular tiling of the hyperbolic plane. An interest of this description is the possibility of intermediate lattices between regular lattices in Euclidean plane and Bethe lattices with the same coordination number. Tome 43 N° 8 15 AVRIL 1982 LE JOURNAL DE PHYSIQUE LETTRES J. Physique LETTRES 43 (1982) L-249 L-25...

The reduced Bethe-Salpeter equation with scalar confinement and vector gluon exchange is applied to quark-antiquark bound states. The so called intrinsic flaw of Salpeter equation with static scalar confinement is investigated. The notorious problem of narrow level spacings is found to be remedied by taking into consideration the retardation effect of scalar confinement. Good fit for the mass s...

Abstract To understand the mechanism of the fermion pair and fermion-antifermion pair condensation,the solutions of Bethe-Salpeter equation in QED3 is examined.In the ladder appoximation our solution for the axial-scalar is consistent with Ward-Takahashi-identity for the axial vector currents.Since the massless scalar-vector sector is described by a coupled integral equation,it is difficult to ...

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 μ. The BS equation is written in the form of an integral equation in the configuration Euclidean x-space with the kernel which for stable bound states M < 2m is a self-adjoint positive operato...