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Topology, Geometry, and Gauge Fields

Interactions

  • Gregory L. Naber

Part of the Applied Mathematical Sciences book series (AMS, volume 141)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Gregory L. Naber
    Pages 1-52
  3. Gregory L. Naber
    Pages 53-160
  4. Gregory L. Naber
    Pages 161-205
  5. Gregory L. Naber
    Pages 207-295
  6. Gregory L. Naber
    Pages 297-350
  7. Gregory L. Naber
    Pages 351-405
  8. Back Matter
    Pages 407-446

About this book

Introduction

This volume is intended to carryon the program initiated in Topology, Geometry, and Gauge Fields: Foundations (henceforth, [N4]). It is written in much the same spirit and with precisely the same philosophical motivation: Mathematics and physics have gone their separate ways for nearly a century now and it is time for this to end. Neither can any longer afford to ignore the problems and insights of the other. Why are Dirac magnetic monopoles in one-to-one correspondence with the principal U(l)­ bundles over S2? Why do Higgs fields fall into topological types? What led Donaldson, in 1980, to seek in the Yang-Mills equations of physics for the key that unlocks the mysteries of smooth 4-manifolds and what phys­ ical insights into quantum field theory led Witten, fourteen years later, to propose the vastly simpler, but apparently equivalent Seiberg-Witten equations as an alternative? We do not presume to answer these questions here, but only to promote an atmosphere in which both mathematicians and physicists recognize the need for answers. More succinctly, we shall endeavor to provide an exposition of elementary topology and geometry that keeps one eye on the physics in which our concepts either arose in­ dependently or have been found to lead to a deeper understanding of the phenomena. Chapter 1 provides a synopsis of the geometrical background we assume of our readers (manifolds, Lie groups, bundles, connections, etc. ).

Keywords

Area Volume gauge theory mathematical physics topology

Authors and affiliations

  • Gregory L. Naber
    • 1
  1. 1.Department of Mathematics and StatisticsCalifornia State UniversityChicoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-6850-3
  • Copyright Information Springer-Verlag New York 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4757-6852-7
  • Online ISBN 978-1-4757-6850-3
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site