Partial-Wave Bethe-Salpeter Equation

The Bethe-Salpeter equation for higher wave bound states of two scalar particles is investigated in the ladder approximation. It is shown that all solutions have the Deser-Gilbert-Sudarshan-Ida integral representation and that they behave like $o\left[{\left(p^2\right)}^{-l-2\mathrm{}}\right]$ as $p^2\to \infty$ apart from a solid harmonic. The angular momentum $l$ is continued to complex values, and it is proved that the wave functions are essentially holomorphic with respect to $l$ in $\mathrm{Re}l>-\frac{1}{4}$. The equation for the Regge trajectories is also discussed.