Geometric Analysis and Applications to Quantum Field Theory

1. Front Matter

   Pages i-ix

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2. Semiclassical Approximation in Chern—Simons Gauge Theory

   • David H. Adams

   Pages 1-20

3. The Knizhnik—Zamolodchikov Equations

   • Peter Bouwknegt

   Pages 21-44

4. Loop Groups and Quantum Fields

   • Alan L. Carey, Edwin Langmann

   Pages 45-94

5. Some Applications of Variational Calculus in Hermitian Geometry

   • Adam Harris

   Pages 95-117

6. Monopoles

   • Michael K. Murray

   Pages 119-135

7. Gromov—Witten Invariants and Quantum Cohomology

   • Yongbin Ruan

   Pages 137-156

8. The Geometry and Physics of the Seiberg—Witten Equations

   • Siye Wu

   Pages 157-203

9. Back Matter

   Pages 205-207

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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.

• Area
• Gauge theory
• Theoretical physics
• Volume
• calculus
• differential equation
• mathematical physics
• minimum

• Department of Physics and Mathematical Physics, Adelaide, Australia

  Peter Bouwknegt

• Department of Pure Mathematics, University of Adelaide, Adelaide, Australia

  Peter Bouwknegt, Siye Wu

• Department of Mathematics, University of Colorado, Boulder, USA

  Siye Wu

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