THE SOURCE GALERKIN METHOD FOR SCALAR FIELD-THEORY

This is part I of a two-part series on the Source Galerkin method. Thi s approach is based on the differential formulation of quantum field t heory. On a finite lattice, the functional differential equations for a theory in the presence of an external source becomes a set of couple d differential equations for the generating functional Z. Systematic a pproximations to these equations are found using the Galerkin method. Calculations are straightforward to perform, and are executed rapidly compared to Monte Carlo. The bulk of the computation involves a single matrix inversion. In addition, bosons and fermions are treated in a s ymmetric manner. In this paper, we consider power series solutions for scalar field theory in D = 2,3,4. Propagators and mass gaps are calcu lated for a number of systems. The calculations in this paper were mad e on a work station of modest power using a fourth order polynomial ex pansion for lattices of size 8(2), 4(3), 2(4) in 2D, 3D, and 4D. In pa rt II we consider the fermionic formulation.