Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

摘要

In this paper we present a summary of results obtained for scalar fieldtheories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QEDand chi^2phi theories are considered. The motivation behind the applicationsdiscussed in this paper is to use the FSR method as a rigorous tool for testingthe quality of commonly used approximations in field theory. Exact calculationsin a quenched theory are presented for one-, two-, and three-body bound states.Results obtained indicate that some of the commonly used approximations, suchas Bethe-Salpeter ladder summation for bound states and the rainbow summationfor one body problems, produce significantly different results from thoseobtained from the FSR approach. We find that more accurate results can beobtained using other, simpler, approximation schemes.