Path Integrals for Potential Scattering

Understand

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.