The Source Galerkin method: fermionic formulation Original Research Article

We present a new deterministic, numerical method to solve fermion field theories. The Source Galerkin approach is based on finding solutions Z [ J] to the lattice functional equations for field theories in the presence of an external source J. Using Grassmann polynomial expansions for the generating functional Z, we calculate propagators for systems of interacting fermions. These calculations are straightforward to perform and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. Because it is not based on a statistical technique, it does not have many of the difficulties often encountered when simulating fermions. Since no determinant is ever calculated, solutions to problems with dynamical fermions are handled more easily. This approach is very flexible, and can be tailored to specific problems based on convenience and computational constraints. We present simple examples to illustrate the method. More general schemes are desirable for more complicated systems.