Perturbative Approach to Scalar Field Theory

Abstract

A practical calculational scheme in quantum field theory is provided by a perturbative expansion in a coupling constant which is supposed to be small. As is well-known, the Feynman diagram method was invented for this purpose in conventional quantum field theory, and in fact reduces considerably the amount of effort required in perturbative calculations. In this chapter, such diagrammatic methods of SQM (called stochastic diagram methods) are presented. Although the additional coordinate in SQM, i.e., the fictitious time, makes stochastic diagrams more complicated than ordinary Feynman ones, the stochastic diagram method is a convenient and indispensable tool in the perturbative study of SQM.