For more than 70 years, quantum field theory (QFT) can be seen as a driving force in the development of theoretical physics. Equally fascinating is the fruitful impact which QFT had in rather remote areas of mathematics. The present book features some of the different approaches, different physically viewpoints and techniques used to make the notion of quantum field theory more precise. For example, the present book contains a discussion including general considerations, stochastic methods, deformation theory and the holographic AdS/CFT correspondence. It also contains a discussion of more recent developments like the use of category theory and topos theoretic methods to describe QFT. The present volume emerged from the 3rd 'Blaubeuren Workshop: Recent Developments in Quantum Field Theory', held in July 2007 at the Max Planck Institute of Mathematics in the Sciences in Leipzig/Germany. All of the contributions are committed to the idea of this workshop series: 'To bring together outstanding experts working in the field of mathematics and physics to discuss in an open atmosphere the fundamental questions at the frontier of theoretical physics'.

Comprehensive exposition of recent ideas and mathematical models in quantum field theory Unique breadth and variety in featuring different aspects to make the notion of QFT more rigorous Articles written in a style that is accessible for non-experts in the field Extensive index over all articles, guaranteeing accessibility to keywords and phrases Includes supplementary material: sn.pub/extras

Autorentext
Prof. Dr. Dr. h.c. Eberhard Zeidler works at the Max Planck Institute for Mathematics in the Sciences in Leipzig (Germany). In 1996 he was one of the founding directors of this institute. He is a member of the Academy of Natural Scientists Leopoldina. In 2006 he was awarded the 'Alfried Krupp Wissenschaftspreis' of the Alfried Krupp von Bohlen und Halbach-Stiftung.

Inhalt
Constructive Use of Holographic Projections.- Topos Theory and 'Neo-Realist' Quantum Theory.- A Survey on Mathematical Feynman Path Integrals: Construction, Asymptotics, Applications.- A Comment on the Infra-Red Problem in the AdS/CFT Correspondence.- Some Steps Towards Noncommutative Mirror Symmetry on the Torus.- Witten's Volume Formula, Cohomological Pairings of Moduli Space of Flat Connections and Applications of Multiple Zeta Functions.- Noncommutative Field Theories from a Deformation Point of View.- Renormalization of Gauge Fields using Hopf Algebras.- Not so Non-Renormalizable Gravity.- The Structure of Green Functions in Quantum Field Theory with a General State.- The Quantum Action Principle in the Framework of Causal Perturbation Theory.- Plane Wave Geometry and Quantum Physics.- Canonical Quantum Gravity and Effective Theory.- From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives.- Towards a q-Deformed Quantum Field Theory.- Towards a q-Deformed Supersymmetric Field Theory.- L ?-Algebra Connections and Applications to String- and Chern-Simons n-Transport.