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
- Standard model of particle physics is derived and its phenomenology discussed
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Physics Studies (MPST)
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About this book
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.
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Table of contents (12 chapters)
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Front Matter
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Noncommutative Geometric Spaces
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Front Matter
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Noncommutative Geometry and Gauge Theories
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Front Matter
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Back Matter
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Noncommutative Geometry and Particle Physics
Authors: Walter D. van Suijlekom
Series Title: Mathematical Physics Studies
DOI: https://doi.org/10.1007/978-94-017-9162-5
Publisher: Springer Dordrecht
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Science+Business Media Dordrecht 2015
Softcover ISBN: 978-94-024-0171-4Published: 27 September 2016
eBook ISBN: 978-94-017-9162-5Published: 21 July 2014
Series ISSN: 0921-3767
Series E-ISSN: 2352-3905
Edition Number: 1
Number of Pages: XVI, 237
Number of Illustrations: 26 b/w illustrations, 2 illustrations in colour
Topics: Mathematical Methods in Physics, Mathematical Physics, Elementary Particles, Quantum Field Theory, Algebraic Geometry