This book contains a collection of essays written in honor of Wolfhart Zimmermann's 80th birthday, most of them based on talks presented at a symposium in his honor. The book shows the unifying force of a subject (Quantum Field Theory) and a person (Zimmermann). It ranges from fundamental questions in quantum physics over applications to particle physics and noncommutative geometry to the latest developments in many body theory and dynamical systems. These key ideas are elucidated by worldwide-recognized experts including Faddeev, Becchi, Buchholz, Lowenstein and Salmhofer. Readers seeking...

Nach einer historisch orientierten Einleitung werden die Grundbegriffe der Quantenfeldtheorie eingefuhrt. Zusammen mit einer Erlauterung der Symmetrien in der klassischen und Quantenphysik bilden sie die Basis zur Darstellung der bekannten Wechselwirkungen: elektromagnetische, schwache und starke. Bemerkungen zur Renormierung erganzen die qualitative Beschreibung. Ziel ist es, die theoretischen Grundlagen der Teilchenphysik moglichst elementar darzulegen."

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...