Noncommutative Geometry and Particle Physics

Walter D. van Suijlekom

ISBN 10: 3031591194 / ISBN 13: 9783031591198

Editore: Springer Nature Switzerland, Springer International Publishing, 2024

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783031591198

Dati bibliografici

• Titolo: Noncommutative Geometry and Particle Physics
• Editore: Springer Nature Switzerland, Springer International Publishing
• Data di pubblicazione: 2024
• Lingua: Inglese
• ISBN 10: 3031591194
• ISBN 13: 9783031591198
• Rilegatura: Buch
• Edizione: seconda edizione
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 24 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 24 millimetri di profondità
• Peso: 662 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

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.