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In the last decade there has been an extraordinary confluence ofideas in mathematics and theoretical physics brought about bypioneering discoveries in geometry and analysis. The various chaptersin this volume, treating the interface of geometric analysis andmathematical physics, represent current research interests. Nosuitable 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-Zamolodchikovequations in conformal field theory (P. Bouwknegt)* Application of the representation theory of loop groups to simplemodels in quantum field theory and to certain integrable systems (A.L.Carey and E. Langmann)* A study of variational methods in Hermitian geometry from theviewpoint of the critical points of action functionals together withphysical 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 inthe above-mentioned areas will benefit from the user-friendlyintroductory style of each chapter as well as the comprehensivebibliographies provided for each topic. Prerequisite knowledge isminimal since sufficient background material motivates each chapter.
Table des matières
Semiclassical Approximation in Chern-Simons Gauge Theory.- The Knizhnik-Zamolodchikov Equations.- Loop Groups and Quantum Fields.- Some Applications of Variational Calculus in Hermitian Geometry.- Monopoles.- Grornov-Witten Invariants and Quantum Cohomology.- The Geometry and Physics of the Seiberg-Witten Equations.
Résumé
In recent years, there has been tremendous progress at the interface
of geometry and mathematical physics. The chapters in this volume
represent current research interests and provide surveys of recent
progress without assuming too much prerequisite knowledge. Sufficient
background motivates each chapter and comprehensive bibliographies are
included making the material accessible to graduate students and
researchers. No suitable succint account of the material is available
elsewhere.
