Bücher der Reihe Mathematical Physics Studies

This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques.The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

Basic properties of oscillatory integrals and the stationary phase method are explained in the book in detail.Those finite-dimensional integrals form a sequence of approximation of the Feynman path integral when the division goes finer and finer.

Proceedings of the Workshop at Shonan, Japan, June 1999

Mathematical Aspects of Quantum Field Theories

This book provides a broad description of the development and (computational) application of many-electron approaches from a multidisciplinary perspective.

In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc.

With these two volumes, the reader will be able to take stock of the present state of the art in a number of subjects at the frontier of current research in mathematics, mathematical physics, and physics.