Boundary Conditions for Schwinger-Dyson Equations and Vacuum Selection

Abstract

When attempting to solve a field theory or matrix model by using Schwinger-Dyson equations, one must address the problem that these equations do not possess a unique solution. This problem came to our attention when trying to numerically solve the equations for certain lattice field theories using a technique known as Source Galerkin [1], which is discussed elsewhere in these proceedings. It was found that to make the numerical method stable, one had to find some way of selecting the right boundary conditions. This led us to the more general question of how the boundary conditions are related to the phase diagram of a field theory or a matrix model. We shall summarize our work on this relation in this paper. Most of the details will appear elsewhere.