Functional treatment of quantum scattering via the dynamical principle

TL;DR

This paper presents a functional approach to quantum scattering using Schwinger's dynamical principle, enabling explicit calculations of asymptotic Green functions for long-range interactions like Coulomb.

Contribution

It introduces a novel functional framework for quantum scattering analysis, particularly addressing long-range potentials with explicit asymptotic Green function derivations.

Findings

Explicit expression for the asymptotic Green function near the energy shell.

Application of the functional method to Coulomb interactions.

Demonstration of the method's effectiveness for long-range potentials.

Abstract

A careful functional treatment of quantum scattering is given using Schwinger's dynamical principle which involves a functional differentiation operation applied to a generating functional written in closed form. For long range interactions, such as for the Coulomb one, it is shown that this expression may be used to obtain explicitly the asymptotic "free" modified Green function near the energy shell.