Overview
- Introduces noncommutative geometry in a novel pedagogical way, starting from finite noncommutative spaces
- Contains a detailed treatment of the applications of noncommutative geometry to gauge theories appearing in high-energy physics
- Derives standard model of particle physics is derived and its phenomenology discussed
Part of the book series: Mathematical Physics Studies (MPST)
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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
About this book
This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. 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.
The second edition of the book contains numerous additional sections and updates. More examples of noncommutative manifolds have been added to the first part to better illustrate the concept of a noncommutative spin manifold and to showcase some of the key results in the field, such as the local index formula. The second part now includes the complete noncommutative geometric description of particle physics models beyond the Standard Model. This addition is particularly significant given the developments and discoveries at the Large Hadron Collider at CERN over the last few years. Additionally, a chapter on the recent progress in formulating noncommutative quantum theory has been included.
The book 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.
Authors and Affiliations
About the author
Dr. W.D. van Suijlekom (Associate Professor), IMAPP - Mathematics.Faculty of Science, Radboud University Nijmegen The NetherlandsExpertise: Mathematical physics; noncommutative geometry, gauge fied theories and particle physics.
Bibliographic Information
Book Title: Noncommutative Geometry and Particle Physics
Authors: Walter D. van Suijlekom
Series Title: Mathematical Physics Studies
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Hardcover ISBN: 978-3-031-59119-8Due: 18 July 2024
Softcover ISBN: 978-3-031-59122-8Due: 18 July 2024
eBook ISBN: 978-3-031-59120-4Due: 18 July 2024
Series ISSN: 0921-3767
Series E-ISSN: 2352-3905
Edition Number: 2
Number of Pages: XVIII, 262
Number of Illustrations: 41 b/w illustrations