Path Integrals for Potential Scattering
Abstract
Two path integral representations for the -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.
Cite
@article{arxiv.0806.3217,
title = {Path Integrals for Potential Scattering},
author = {R. Rosenfelder},
journal= {arXiv preprint arXiv:0806.3217},
year = {2009}
}
Comments
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)