Path-integral formulation of scattering theory

Abstract

A new formulation of nonrelativistic scattering theory is developed which expresses the $S$ matrix as a path integral. This formulation appears to have at least two advantages: (1) A closed formula is obtained for the $S$ matrix in terms of the potential, not involving a series expansion; (2) the energy-conserving $\ensuremath{\delta}$ function can be explicitly extracted using a technique analogous to that of Faddeev and Popov, thereby yielding a closed path-integral expression for the $T$ matrix. The introduction of the concept of the classical interaction picture provides considerable physical insight into this formulation. This formulation also suggests a successionof improvements to the eikonal approximation, the first of which is discussed explicitly.