Feynman-Schwinger technique in field theories

In these lectures we introduce the Feynman-Schwinger representation method for solving nonperturbative problems in field theory. As an introduction we first give a brief overview of integral equations and path integral methods for solving nonperturbative problems. Then we discuss the Feynman-Schwinger (FSR) representation method with applications to scalar interactions. The FSR approach is a continuum path integral integral approach in terms of covariant trajectories of particles. Using the exact results provided by the FSR approach we test the reliability of commonly used approximations for nonperturbative summation of interactions for few body systems.