Complex Differential Geometry and Supermanifolds in Strings and Fields

This volume deals with one of the most active fields of research in mathematical physics: the use of geometric and topological methods in field theory. The emphasis in these proceedings is on complex differential geometry, in particular on Kähler manifolds, supermanifolds, and graded manifolds. From the point of view of physics the main topics were field theory, string theory and problems from elementary particle theory involving supersymmetry. The lectures show a remarkable unity of approach and are considerably related to each other. They should be of great value to researchers and graduate students.

Inhalt
Supersymmetric sigma models and Kähler manifolds.- Nonlinear realizations, Kähler manifolds and the Virasoro manifold.- In search of the graded manifold of maps between graded manifolds.- Path integration in superspace.- Supermanifolds, supersymmetry and berezin integration.- Berezin integration and dimensional reduction.- Aspects of string theory.- Field and string quantization in curved space-tines.