Path-integral formulation of scattering theory: Central potentials

We consider central-potential scattering and determine a path-integral representation for the $S$ matrix in polar coordinates. This is obtained by transforming to polar coordinates a Cartesian form of the nonrelativistic $S$ matrix given by Campbell et al., and implementing an idea of Faddeev to obtain the appropriate asymptotic conditions. Our results are applied to scattering in an inverse-square potential to determine the correct phase shifts as well as the $S$ matrix.