Relativistic confinement in a Bethe-Salpeter model

Abstract

Starting with a confinement kernel originally due to Henley, we use the instantaneous approximation to reduce the Bethe-Salpeter equation for bosons to an ordinary second-order differential equation. In the nonrelativistic limit the equation reduces to that for a spherically symmetric simple harmonic oscillator. For the relativistic equation, we obtain an asymptotic series for the energy levels of the bound states valid in the strong-coupling limit. Our results are in qualitative agreement with the numerical results for a similar system studied by Henley.