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Noncommutative Geometry and the Standard Model of Elementary Particle Physics

  • Book
  • © 2002

Overview

Editors:
  1. Florian Scheck

    1. Institut für Physik, Theoretische Elementarteilchenphysik, Johannes Gutenberg-Universität Mainz, Mainz, Germany

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  2. Harald Upmeier

    1. Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

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  3. Wend Werner

    1. Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Germany

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  • Bridges the gap between standard textbook material and the forefront of research
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics (LNP, volume 596)

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Table of contents (18 chapters)

  1. Front Matter

    Pages I-XII
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  2. Foundations of Noncommutative Geometry and Basic Model Building

    1. Front Matter

      Pages 1-1
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    2. Spectral Triples and Abstract Yang-Mills Functional

      • Ralf Holtkamp
      Pages 4-10

    3. Real Spectral Triples and Charge Conjugation

      • Ralf Meyer
      Pages 11-20

    4. The Commutative Case: Spinors, Dirac Operator and de Rham Algebra

      • Michael Frank
      Pages 21-39

    5. Connes’ Trace Formula and Dirac Realization of Maxwell and Yang-Mills Action

      • Peter M. Alberti, Reiner Matthes
      Pages 40-74

    6. The Einstein-Hilbert Action as a Spectral Action

      • Bernd Ammann, Christian Bär
      Pages 75-108

    7. Spectral Action and the Connes-Chamsedinne Model

      • Ryszard Nest, Elmar Vogt, Wend Werner
      Pages 109-132

  3. The Lagrangian of the Standard Model Derived from Noncommutative Geometry

    1. Front Matter

      Pages 134-134
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    2. Dirac Operator and Real Structure on Euclidean and Minkowski Spacetime

      • Herald Upmeier
      Pages 136-151

    3. The Electro-weak Model

      • Karen Elsner, Holger Neumann, Harald Upmeier
      Pages 152-171

    4. The Full Standard Model

      • Karen Elsner, Holger Neumann, Harald Upmeier
      Pages 172-215

    5. Standard Model Coupled with Gravity

      • Holger Neumann, Harald Upmeier
      Pages 216-229

    6. The Higgs Mechanism and Spontaneous Symmetry Breaking

      • Florian Scheck
      Pages 230-240

  4. New Directions in Noncommutative Geometry and Mathematical Physics

    1. Front Matter

      Pages 242-242
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    2. The Impact of NC Geometry in Particle Physics

      • Bruno Iochum
      Pages 244-259

    3. The su(2|1) Model of Electroweak Interactions and Its Connection to NC Geometry

      • Rainer Häussling
      Pages 260-270

    4. Quantum Fields and Noncommutative Spacetime

      • Klaus Fredenhagen
      Pages 271-277

    5. NC Geometry and Quantum Fields: Simple Examples

      • Edwin Langmann
      Pages 278-298

    6. Dirac Eigenvalues as Dynamical Variables

      • Giovanny Landi
      Pages 299-312
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Keywords

About this book

The outcome of a close collaboration between mathematicians and mathematical physicists, these lecture notes present the foundations of A. Connes noncommutative geometry as well as its applications in particular to the field of theoretical particle physics. The coherent and systematic approach makes this book useful for experienced researchers and postgraduate students alike.

Editors and Affiliations

  • Institut für Physik, Theoretische Elementarteilchenphysik, Johannes Gutenberg-Universität Mainz, Mainz, Germany

    Florian Scheck

  • Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Marburg, Germany

    Harald Upmeier

  • Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Germany

    Wend Werner

Bibliographic Information

  • Book Title: Noncommutative Geometry and the Standard Model of Elementary Particle Physics

  • Editors: Florian Scheck, Harald Upmeier, Wend Werner

  • Series Title: Lecture Notes in Physics

  • DOI: https://doi.org/10.1007/3-540-46082-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Hardcover ISBN: 978-3-540-44071-0Published: 26 November 2002

  • Softcover ISBN: 978-3-642-07897-2Published: 08 December 2010

  • eBook ISBN: 978-3-540-46082-4Published: 11 January 2008

  • Series ISSN: 0075-8450

  • Series E-ISSN: 1616-6361

  • Edition Number: 1

  • Number of Pages: XII, 350

  • Topics: Mathematical Methods in Physics, Differential Geometry, Elementary Particles, Quantum Field Theory, Algebra

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