Noncommutative Geometry and Particle Physics

1. Front Matter

   Pages i-xvi

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2. Introduction

   • Walter D van Suijlekom

   Pages 1-5

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3. Noncommutative Geometric Spaces

   1. Front Matter

      Pages 7-7

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   2. Finite Noncommutative Spaces

      • Walter D. van Suijlekom

      Pages 9-30

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   3. Finite Real Noncommutative Spaces

      • Walter D. van Suijlekom

      Pages 31-47

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   4. Noncommutative Riemannian Spin Manifolds

      • Walter D. van Suijlekom

      Pages 49-74

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   5. The Local Index Formula in Noncommutative Geometry

      • Walter D. van Suijlekom

      Pages 75-99

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4. Noncommutative Geometry and Gauge Theories

   1. Front Matter

      Pages 101-101

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   2. Gauge Theories from Noncommutative Manifolds

      • Walter D. van Suijlekom

      Pages 103-119

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   3. Spectral Invariants

      • Walter D. van Suijlekom

      Pages 121-135

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   4. Almost-Commutative Manifolds and Gauge Theories

      • Walter D. van Suijlekom

      Pages 137-158

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   5. The Noncommutative Geometry of Electrodynamics

      • Walter D van Suijlekom

      Pages 159-174

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   6. The Noncommutative Geometry of Yang–Mills Fields

      • Walter D. van Suijlekom

      Pages 175-184

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   7. The Noncommutative Geometry of the Standard Model

      • Walter D. van Suijlekom

      Pages 185-212

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   8. Phenomenology of the Noncommutative Standard Model

      • Walter D. van Suijlekom

      Pages 213-230

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5. Back Matter

   Pages 231-237

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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.

• 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

• IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands

  Walter D. van Suijlekom

Dr. W.D. van Suijlekom (Assistant Professor/VIDI-Laureate) IMAPP - Mathematics Faculty of Science, Radboud University Nijmegen The Netherlands Expertise: Mathematical physics; noncommutative geometry, gauge field theories and particle physics.

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