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Geometric Analysis and Applications to Quantum Field Theory

  • Peter Bouwknegt
  • Siye Wu

Part of the Progress in Mathematics book series (PM, volume 205)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Peter Bouwknegt
    Pages 21-44
  3. Alan L. Carey, Edwin Langmann
    Pages 45-94
  4. Michael K. Murray
    Pages 119-135
  5. Back Matter
    Pages 205-207

About this book

Introduction

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.

Keywords

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

Editors and affiliations

  • Peter Bouwknegt
    • 1
    • 2
  • Siye Wu
    • 2
    • 3
  1. 1.Department of Physics and Mathematical PhysicsAdelaideAustralia
  2. 2.Department of Pure MathematicsUniversity of AdelaideAdelaideAustralia
  3. 3.Department of MathematicsUniversity of ColoradoBoulderUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0067-3
  • Copyright Information Birkhäuser Boston 2002
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6597-9
  • Online ISBN 978-1-4612-0067-3
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site
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