Extension of Weinberg's quasi-particle theory to standing waves

Abstract

In the context of a potential, a resume of scattering theory is developed along two alternative lines, either (a) by the resolvent of the Lippmann-Schwinger equation, leading to the reaction matrixT, or (b) by a modified resolvent associated with standing waves, leading to the reactance matrixK. On this basis it is shown that Weinberg's theory of quasi-particles, which was originally appropriate to the scheme (a), has a counterpart in the scheme (b), in which the quasi-particle states are standing waves, and the result is a quasi-Born expansion ofK. The equations for passing between schemes (a) and (b) are developed. It is argued that the quasi-particle theory of scheme (b) possesses some advantages of simplicity.