Path Integrals for Potential Scattering

Abstract

Two path integral representations for the $T$-matrix in nonrelativistic potential scattering are derived and proved to produce the complete Born series when expanded to all orders. They are obtained with the help of "phantom" degrees of freedom which take away explicit phases that diverge for asymptotic times. In addition, energy conservation is enforced by imposing a Faddeev-Popov-like constraint in the velocity path integral. These expressions may be useful for attempts to evaluate the path integral in real time and for alternative multiple scattering expansions. Standard and novel eikonal-type high-energy approximations and systematic expansions immediately follow.

31 pages, 3 figures, Latex;v2: typo in eq. (4.6) corrected, references updated;v3: misprints corrected, small changes in text following referee comments and PR style conventions (except some idiosyncrasies), matches published version + typo correction in eq. (88)

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Cited by in corpus (10)

• A New Path-Integral Representation of the $T$-Matrix in Potential Scattering
• Unifying approaches: derivation of Balitsky hierarchy from the Lipatov effective action
• Variational Approximations in a Path-Integral Description of Potential Scattering
• Variational Methods for Path Integral Scattering
• Scattering Theory with Path Integrals
• Exact Path-Integral Representations for the $T$-Matrix in Nonrelativistic Potential Scattering
• Path Integrals in Quantum Physics
• Scattering using real-time path integrals
• Validity of Born Approximation for Nuclear Scattering in Path Integral Representation
• On the numerical evaluation of real-time path integrals: Double exponential integration and the Maslov correction