Interacting Quantum Fields

Abstract

The previous chapters were dedicated to the quantization of free wave fields. The presentation of a detailed introduction to the relevant techniques is the main goal of this book. It cannot be overlooked, however, that the description of free fields on their own is a rather trivial task. The emergence of interesting physical processes can only be expected if there are interactions among the fields. From a mathematical point of view this happens if the Lagrangian contains more complicated parts that go beyond the bilinear terms encountered so far. Such terms may consist of higher powers of the field function (describing self-interactions) or of products involving fields of different kinds. Within the framework of classical theory this leads to a nonlinear field equation or coupled systems of field equations which are difficult to solve.