The Source Galerkin method finds approximate solutions to the functional differential equations of field theories in the presence of external sources. While developing this process, it was recognized that approximations of the spectral representation
s of the Greens functions by Sinc function expansions are an extremely powerful calculative tool. Specifically, this understanding makes it not only possible to apply the Source Galerkin method to higher dimensional field theories, but also leads to a new approach to perturbation theory calculations in scalar and fermionic field theories. This report summarizes the methodologies for solving quantum field theories with the Source Galerkin method and for performing perturbation theory calculations using Sinc approximations.
The Source Galerkin Method is a new numerical technique that is being developed to solve Quantum Field Theories on the continuum. It is not based on Monte Carlo techniques and has a measure to evaluate relative errors. It promises to increase the acc
uracy and speed of calculations, and takes full advantage of symmetries of the theory. The application of this method to the non-linear sigma model is outlined.
