Studying the Bethe–Salpeter formalism for interactions instantaneous in the rest frame of the bound states described, we show that, for bound-state constituents of arbitrary masses, the mass of the ground state of a given spin may be calculated almost entirely analytically with high accuracy, without the (numerical) diagonalization of the matrix representation obtained by expansion of the solut...

The spinless Salpeter equation represents the simplest, and most straightforward, generalization of the Schrödinger equation of standard nonrelativistic quantum theory towards the inclusion of relativistic kinematics. Moreover, it can be also regarded as a well-defined approximation to the Bethe–Salpeter formalism for descriptions of bound states in relativistic quantum field theories. The corr...

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...

We study the eigenvalues En` of the Salpeter Hamiltonian H = β √ m2 + p2 +vr, v > 0, β > 0, in three dimensions. By using geometrical arguments we show that, for suitable values of P, here provided, the simple semi-classical formula En` ≈ min r>0 { v(Pn`/r) 2 + β √ m2 + r2 } provides both upper and lower energy bounds for all the eigenvalues of the problem. PACS: 03.65.Ge, 03.65.Pm, 11.10.St En...

Bethe-Salpeter equation in the non-commutative space for a scalarscalar bound state is considered. It is shown that in the non-relativistic limit, the effect of spatial non-commutativity appears as if there exist a magnetic dipole moment coupled to each particle. e-mail: [email protected] e-mail: [email protected] Non-commutativity of space-time has been recently a subject of intense ...

We obtain lower bounds on the ground state energy, in one and three dimensions, for the spinless Salpeter equation (Schrödinger equation with a relativistic kinetic energy operator) applicable to potentials for which the attractive parts are in L(R) for some p > n (n = 1 or 3). An extension to confining potentials, which are not in L(R), is also presented.

A method to compute the scattering solutions of a spinless Salpeter equation ~or a Schrödinger equation! with a central interaction is presented. This method relies on the three-dimensional Fourier grid Hamiltonian method used to compute bound states. It requires only the evaluation of the potential at equally spaced grid points and yields the radial part of the scattering solution at the same ...

We derive a confining qq̄ Bethe–Salpeter equation starting from the same assumptions on the Wilson loop integral already adopted in the derivation of a semirelativistic heavy quark potential. We show that, by standard approximations, an effective meson squared mass operator can be obtained from our BS kernel and that, from this, by 1 m 2 expansion, the corresponding Wilson loop potential is reco...