Geometric Analysis and Applications to Quantum Field Theory

In the last decade there has been an extraordinary confluence of ideas in mathematics and theoretical physics brought about by pioneering discoveries in geometry and analysis. The various chapters in this volume, treating the interface of geometric analysis and mathematical physics, represent current research interests. No suitable succinct account of the material is available elsewhere. Key topics include: A self-contained derivation of the partition function of Chern- Simons gauge theory in the semiclassical approximation (D.H. Adams) Algebraic and geometric aspects of the Knizhnik-Zamolodchikov equations in conformal field theory (P. Bouwknegt) Application of the representation theory of loop groups to simple models in quantum field theory and to certain integrable systems (A.L. Carey and E. Langmann) A study of variational methods in Hermitian geometry from the viewpoint of the critical points of action functionals together with physical backgrounds (A. Harris) A review of monopoles in nonabelian gauge theories (M.K. Murray) Exciting developments in quantum cohomology (Y. Ruan) * The physics origin of Seiberg-Witten equations in 4-manifold theory (S. Wu) Graduate students, mathematicians and mathematical physicists in the above-mentioned areas will benefit from the user-friendly introductory style of each chapter as well as the comprehensive bibliographies provided for each topic. Prerequisite knowledge is minimal since sufficient background material motivates each chapter.

Inhalt

Preface D. H. Adams: Semiclassical Approximation in Chern--Simons Gauge Theory P. Bouwknegt: The Knizhnik--Zamolodchikov Equations A. L. Carey and E. Langmann: Loop Groups and Quantum Fields A. Harris: Some Applications of Variational Calculus in Hermitian Geometry M. K. Murray: Monopoles Y. Ruan: Gromov--Witten Invariants and Quantum Cohomology * S. Wu: The Geometry and Physics of the Seiberg--Witten Equations