Noncommutative Geometry and Particle Physics: Mathematical Physics Studies
Autor Walter D. van Suijlekomen Limba Engleză Hardback – 4 aug 2014
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Specificații
ISBN-13: 9789401791618
ISBN-10: 9401791619
Pagini: 253
Ilustrații: XVI, 237 p. 28 illus., 2 illus. in color.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.54 kg
Ediția:2015
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematical Physics Studies
Locul publicării:Dordrecht, Netherlands
ISBN-10: 9401791619
Pagini: 253
Ilustrații: XVI, 237 p. 28 illus., 2 illus. in color.
Dimensiuni: 155 x 235 x 20 mm
Greutate: 0.54 kg
Ediția:2015
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematical Physics Studies
Locul publicării:Dordrecht, Netherlands
Public țintă
GraduateCuprins
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.
Notă biografică
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.
Textul de pe ultima copertă
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.
Caracteristici
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