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 8 matrix in terms of the potential, not involving a series expansion; (2) the energy-conserving 8 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.
We generalize the path integral formalism of quantum mechanics to include the use of arbitrary infinitesimal generators, thus providing explicit expressions for solutions of a wide class of differential equations. In particular, we develop a method of calculating the eigenfunctions of a large class of operators.
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We develop a.Reggeizedmodel for the 3-to-3 amplitude using group theoretical variables. The triple-Regge vertex is defined by the asymptotic form of the amplitude. We show that the Veneziano model has the asymptotic form predicted by our model .
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