Path Integrals and Effective Theories

Abstract

To an increasing extent the canonical quantization of fields is replaced by path integral representations. It is assumed that path integrals not only implicitly contain the quantization rules but also offer the complete solution of quantum field dynamics, i.e. they should describe all possible field configurations and processes. In particular with respect to composite particle dynamics they should implicitly contain all effective theories describing composite particle processes. Thus the “only” problem is the evaluation of such path integrals. Although great efforts have been made with respect to their numerical evaluation, for complicated systems, e.g. for interacting composite particles, one cannot circumvent the analytical treatment.