1999/03/22 by J. Gasser, G. Wanders · 2 citations
Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Essential singularity #Infinitesimal #Interval (graph theory) #Nonlinear Photonic Systems #Nonlinear system #Quantum many-body systems #Singularity #Uniqueness #hep-ph
paper · pdf · doi:10.1007/s100529900086
published as Eur.Phys.J.C10:159-173,1999 · 36 pages (LaTex), 9 figures embedded with epsfig.sty
arxiv created 1999/03/22 · openalex publication_date 1999/08/01 · arxiv updated 2011/09/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The Roy equation in the single channel case is a nonlinear, singular integral equation for the phase shift in the low-energy region. We first investigate the infinitesimal neighborhood of a given solution, and then present explicit expressions for amplitudes that satisfy the nonlinear equation exactly. These amplitudes contain free parameters that render the non-uniqueness of the solution manifest. They display, however, an unphysical singularity at the upper end of the interval considered. This singularity disappears and uniqueness is achieved if one uses analyticity properties of the amplitudes that are not encoded in the Roy equation.