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Geometric Analysis and Applications to Quantum Field Theory

  • Textbook
  • © 2002

Overview

Editors:
  1. Peter Bouwknegt

    1. Department of Physics and Mathematical Physics, Adelaide, Australia
      Department of Pure Mathematics, University of Adelaide, Adelaide, Australia

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    You can also search for this editor in PubMed   Google Scholar

  2. Siye Wu

    1. Department of Pure Mathematics, University of Adelaide, Adelaide, Australia
      Department of Mathematics, University of Colorado, Boulder, USA

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

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

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Table of contents (7 chapters)

  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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Keywords

About this book

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.

Editors and Affiliations

  • 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

Bibliographic Information

  • Book Title: Geometric Analysis and Applications to Quantum Field Theory

  • Editors: Peter Bouwknegt, Siye Wu

  • Series Title: Progress in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0067-3

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2002

  • Hardcover ISBN: 978-0-8176-4287-7Published: 08 February 2002

  • Softcover ISBN: 978-1-4612-6597-9Published: 01 November 2012

  • eBook ISBN: 978-1-4612-0067-3Published: 06 December 2012

  • Series ISSN: 0743-1643

  • Series E-ISSN: 2296-505X

  • Edition Number: 1

  • Number of Pages: IX, 207

  • Topics: Geometry, Analysis, Applications of Mathematics, Theoretical, Mathematical and Computational Physics

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