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 StandardModel of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.
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.
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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
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ISBN
9789402401714
Publisert
2016-09-27
Utgiver
Springer
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Graduate, E, 04
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
16
Forfatter