Nonperturbative path-integral approximations

A nonperturbative path-integral approximation scheme is introduced heuristically, and then interpreted from the point of view of Feynman path integrals. The utility and the properties of the technique are explored by application to three widely different problems. When applied to the problem of a bound charged particle in an electromagnetic field, the method yields the momentum-translation approximation plus corrections. For high-energy scattering, the technique gives immediately the standard eikonal results, and also suggests corrections. For a charged free particle in an electromagnetic field, the method in simplest form leads to an approximation to the exact Volkov solution, and correction terms yield precisely the Volkov solution.