Solving the homogeneous Bethe-Salpeter equation

We study a method for solving the homogeneous Bethe-Salpeter equation. By introducing a ``fictitious'' eigenvalue \ensuremath{\lambda} the homogeneous Bethe-Salpeter equation is interpreted as a linear eignevalue equation, where the bound state mass is treated as an input parameter. Using the improved ladder approximation with a constant fermion mass, we extensively study the spectrum of the fictitious eigenvalue \ensuremath{\lambda} for the vector bound states and find the discrete spectrum for a vanishing bound state mass. We also evaluate the bound state masses by tuning the appropriate eigenvalue to be unity, and find massless vector bound states for specific values of the constant fermion masses. \textcopyright{} 1996 The American Physical Society.