Convergence of Padé Approximants for the Bethe-Salpeter Amplitude

Abstract

We extend some earlier work on the Bethe-Salpeter equation to show that the sequence of [$N, N$] Pad\'e approximants to ${tan\ensuremath{\delta}}_{l}$ converges to the correct result if the scattered particles are of equal mass. The proof includes a demonstration that the symmetrized kernel of the Bethe-Salpeter equation after a coordinatespace Wick rotation is ${L}^{2}$. An interesting connection between Pad\'e approximants and the Schwinger variational principle is given.