Noncommutative Geometry and Particle Physics

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Beschreibung

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.

Über den Autor

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.

Zusammenfassung

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: [...]

Inhaltsverzeichnis

Preface.- Introduction.- Part 1. Noncommutative geometric spaces.- Finite noncommutative spaces.- Finite real noncommutative spaces.- Noncommutative Riemannian spin manifolds.- The local index formula in noncommutative geometry.- Part 2. Noncommutative geometry and gauge theories.- Gauge theories from noncommutative manifolds.- Spectral invariants.- Almost-commutative manifolds and gauge theories.- The noncommutative geometry of electrodynamics.- The noncommutative geometry of Yang-Mills fields.- The noncommutative geometry of the Standard Model.- Phenomenology of the noncommutative Standard Model.- Bibliography.

Details

Erscheinungsjahr:	2014
Fachbereich:	Astronomie
Genre:	Physik
Rubrik:	Naturwissenschaften & Technik
Thema:	Lexika
Medium:	Buch
Seiten:	256
Reihe:	Mathematical Physics Studies
Inhalt:	xvi 237 S. 26 s/w Illustr. 2 farbige Illustr. 237 p. 28 illus. 2 illus. in color.
ISBN-13:	9789401791618
ISBN-10:	9401791619
Sprache:	Englisch
Herstellernummer:	86212367
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Suijlekom, Walter D. van
Auflage:	2015
Hersteller:	Springer Netherland Springer Netherlands Mathematical Physics Studies
Maße:	241 x 160 x 20 mm
Von/Mit:	Walter D. van Suijlekom
Erscheinungsdatum:	04.08.2014
Gewicht:	0,553 kg

preigu-id: 105210492