Renormalization of quantum field theories with non-linear field transformations

the long version

The characteristic feature of many models for field theories based on concepts of differential geometry is their nonlinearity. In this book a systematic exposition of nonlinear transformations in quantum field theory is given. The book starts with a short account of the renormalization theory with examples which can be handled successfully in four space-time dimensions. The second part is devoted to nonlinear sigma-models and their constructions in two dimensions. In the final section geometrical and cohomological methods and the relations to string theory are treated. This book is an important contribution towards rigorous definitions, and the mastering of nonlinear reparametrizations in agreement with the principles of quantum field theory will help to deal with anomalies, geometry and the like consistently and thus to understand better their implications for physics. The collection of papers addresses researchers and graduate students as well and will stimulate further work on the foundations of quantum field theory.