Path-integral Formulation of Scattering Theory

Authors

Paul Finkler, University of Nebraska-LincolnFollow
C. Edward Jones, University of Nebraska-Lincoln
M. Misheloff, University of Nebraska-Lincoln

Document Type

Article

Date of this Version

10-15-1975

Citation

Physical Review D (October 1975) 12(8): 15

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 δ function can be explicitly extracted using a technique analogous to that of Faddeev and Popov, thereby yielding a closed pathintegral 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.