Analytic Continuation in Complex Angular Momentum and Integral Equations

Abstract

An attack is made on the problem of the analytic continuation in the angular momentum variable $l$ of amplitudes defined by integral equations beyond the value of $\mathrm{Re}l$ at which the kernel ceases to be of the Schmidt type and the Fredholm theory cannot be applied. A general technique is developed and applied to the Yukawa potential case and to the ladder graph series in the ${\varphi }^3$ theory. In both cases meromorphy is established for $\mathrm{Re}l>-\frac{5}{2}$ and a procedure is indicated for a stepwise continuation to the entire $l$ plane.