Source driven solutions of quantum field theories

A program is described to develop a new numerical approach to the solution of quantum field theories which is called the Source Galerkin method. Source Galerkin has strengths which should allow its application to problems, such as scattering predictions, that require too much computing power to be examined by other methods at this time. Unlike Monte Carlo evaluations, Source Galerkin is equally suited for studying fermionic or bosonic problems. Further, at least in lower dimensions, a continuum formulation of Source Galerkin is straightforward. While Source Galerkin implementations appear to be relatively economical in their use of computer cycles, they require complicated algebraic set up procedures for each problem examined. The full solution set can be obtained by appropriate continuations of the integration regions into the complex plane. This insight was a result of the very detailed and specific understanding of a theory that is necessary in order to numerically perform evaluations using Source Galerkin methods. (R.P.)