An exact form is presented for the axial-vector Bethe-Salpeter equation, which is valid when the quark-gluon vertex is fully dressed. A Ward-Takahashi identity for the Bethe-Salpeter kernel is derived therefrom and solved for a class of dressed quark-gluon-vertex models. The solution provides a symmetry-preserving closed system of gap and vertex equations. The analysis can be extended to the ve...

We show how the invariance under the charge conjugation and CPT symmetry, present in the Bethe-Salpeter equation, is lost in the reduction to certain relativistic three-dimensional equations. This in particular leads to the breakdown of the standard Lorentz structure and renormalization procedures for the resulting single-particle propagators. We formulate the equal-time approximation of the Be...

Recently an instantaneous approximation to the Bethe–Salpeter formalism for the analysis of bound states in quantum field theory has been proposed which retains, in contrast to the Salpeter equation, as far as possible the exact propagators of the bound-state constituents, extracted nonperturbatively from Dyson–Schwinger equations or lattice gauge theory. The implications of this improvement fo...

We study the spectrum of the Salpeter Hamiltonian H = β √ m2 + p2 +V (r), where V (r) is an attractive central potential in three dimensions. If V (r) is a convex transformation of the Coulomb potential −1/r and a concave transformation of the harmonic-oscillator potential r, then upper and lower bounds on the discrete eigenvalues of H can be constructed, which may all be expressed in the form ...

In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy levels and wave functions. These theorems are applied to the prototype of all relativistic wave equations, the spinless Salpeter equation. PACS : 11.10.St, 03.65...

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...