Exact Path-Integral Representations for the $T$-Matrix in Nonrelativistic Potential Scattering

Details Exact Path-Integral Representations for the $T$-Matrix in Nonrelativistic Potential Scattering Exact Path-Integral Representations for the $T$-Matrix in Nonrelativistic Potential Scattering

2010-08-10

arxiv.org/abs/1008.1718v2

Few Body Syst.49:41-50,2011

Physics

Nuclear Physics

Nuclear Theory

6 pages, 2 figures. Contribution to the workshop "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics",

Scientific paper

10.1007/s00601-010-0104-x

Several path integral representations for the $T$-matrix in nonrelativistic potential scattering are given which produce the complete Born series when expanded to all orders and the eikonal approximation if the quantum fluctuations are suppressed. They are obtained with the help of "phantom" degrees of freedom which take away explicit phases that diverge for asymptotic times. Energy conservation is enforced by imposing a Faddeev-Popov-like constraint in the velocity path integral. An attempt is made to evaluate stochastically the real-time path integral for potential scattering and generalizations to relativistic scattering are discussed.

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