Noncommutative Geometry and Particle Physics

Walter D. van Suijlekom (Autor)

Buch | Softcover

237 Seiten

2016 | Softcover reprint of the original 1st ed. 2015
Springer (Verlag)
978-94-024-0171-4 (ISBN)

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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.

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.

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.

Erscheinungsdatum	04.03.2022
Reihe/Serie	Mathematical Physics Studies
Zusatzinfo	2 Illustrations, color; 26 Illustrations, black and white
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Hochenergiephysik / Teilchenphysik
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
ISBN-10	94-024-0171-7 / 9402401717
ISBN-13	978-94-024-0171-4 / 9789402401714
Zustand	Neuware