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Noncommutative Geometry and Particle Physics

  • Walter D. van Suijlekom

Part of the Mathematical Physics Studies book series (MPST)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Walter D van Suijlekom
    Pages 1-5
  3. Noncommutative Geometric Spaces

    1. Front Matter
      Pages 7-7
    2. Walter D. van Suijlekom
      Pages 9-30
    3. Walter D. van Suijlekom
      Pages 31-47
    4. Walter D. van Suijlekom
      Pages 49-74
    5. Walter D. van Suijlekom
      Pages 75-99
  4. Noncommutative Geometry and Gauge Theories

    1. Front Matter
      Pages 101-101
    2. Walter D. van Suijlekom
      Pages 103-119
    3. Walter D. van Suijlekom
      Pages 121-135
    4. Walter D. van Suijlekom
      Pages 137-158
    5. Walter D van Suijlekom
      Pages 159-174
    6. Walter D. van Suijlekom
      Pages 175-184
    7. Walter D. van Suijlekom
      Pages 185-212
    8. Walter D. van Suijlekom
      Pages 213-230
  5. Back Matter
    Pages 231-237

About this book

Introduction

This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.         

Keywords

Abelian Gauge Theories Connes' Reconstruction Theorem Cyclic Cohomology K-theory of C* Algebras Local Index Formula Non-abelian Gauge Theories Non-commutative Geometry Non-commutative Manifolds Unitary and Morita Equivalence of Spectral Triples Yang–Mills Gauge Theory

Authors and affiliations

  • Walter D. van Suijlekom
    • 1
  1. 1.IMAPPRadboud University NijmegenNijmegenThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-9162-5
  • Copyright Information Springer Science+Business Media Dordrecht 2015
  • Publisher Name Springer, Dordrecht
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-94-017-9161-8
  • Online ISBN 978-94-017-9162-5
  • Series Print ISSN 0921-3767
  • Series Online ISSN 2352-3905
  • Buy this book on publisher's site