Divergences in Perturbation Theory

Abstract

Loop corrections to the tree level results turn out to be divergent, or very large in certain cases. The physical reason for these divergences is that the system interacts with an infinite (or very large) number of fluctuating degrees of freedom. The problematic divergences emerge in the calculation of per se finite quantities. This kind of divergence signals that the perturbation theory is organized in an inappropriate way. This chapter explains the large flexibility of the perturbative renormalization and the concept of the line of constant physics, which represent the guiding “compass” for extracting unique physical predictions from different models in the theory space. The principles are explained through the detailed example of the self-interacting one-component scalar field theory.