Ordinary (abelian) theta functions describe the properties of moduli spaces of one-dimensional vector bundles on algebraic curves. Non-abelian theta functions, which are the main topic of this book, play a similar role in the study of higher-dimensional vector bundles. The book describes various aspects of the theory of non-abelian theta functions and the moduli spaces of vector bundles, including their applications to problems of quantization and to classical and quantum conformal field theories.

The book is an important source of information for specialists in algebraic geometry and its application to mathematical aspects of quantum field theory.

Readership

Graduate students and research mathematicians interested in algebraic geometry and its applications to mathematical physics.