Dispersion Relations for Dirac Potential Scattering

Publisher Website
Google Scholar
Abstract
Dispersion relations for scattering of a Dirac particle by a potential are shown to hold for a broad class of potentials. In contrast to the field theoretic case, the derivation here makes no use of the concept of causality but is instead based directly on the analytic properties of the Fredholm solution of the scattering integral equation. It is shown that the scattering amplitude, considered as a function of energy and momentum transfer, can be extended to a function analytic in the complex energy plane, for real momentum transfer. The dispersion relations then follow in the standard way from Cauchy's theorem. The final results involve one "subtraction." It is also shown that the analytic continuation into the unphysical region for nonforward scattering can be carried out by means of a partial wave expansion.