Stephen Bruce Sontz: Principal Bundles

Cover: 9783319147642 | Principal Bundles | The Classical Case | Stephen Bruce Sontz | Buch

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Sprache: Englisch

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Beschreibung

This introductory graduate level text provides a relatively quick path to a special topic in classical differential geometry: principal bundles. While the topic of principal bundles in differential geometry has become classic, even standard, material in the modern graduate mathematics curriculum, the unique approach taken in this text presents the material in a way that is intuitive for both students of mathematics and of physics. The goal of this book is to present important, modern geometric ideas in a form readily accessible to students and researchers in both the physics and mathematics communities, providing each with an understanding and appreciation of the language and ideas of the other.

Über den Autor

Stephen Bruce Sontz received a Ph.D. from the University of Virginia with a dissertation in mathematical physics. He has published around 25 research articles in that field as well as two textbooks with Springer. These are "Quantum Principal Bundles, The Classical Case" and "Quantum Principal Bundles, The Quantum Case". He is a research professor at the Centro de Investigación en Matemáticas, A.C. (CIMAT) in Guanajuato, Mexico. He also teaches undergraduate courses in the Mathematics Department of the University of Guanajuato, where he has given courses using the material in this book.

Zusammenfassung

Provides a relatively quick path to a special topic in differential geometry: principal bundles, whose properties are then described in some detail

Presents important, modern geometric ideas in a form accessible to students and researchers in other areas

No previous knowledge of differential geometry is assumed

Inhaltsverzeichnis

Introduction.- Basics of Manifolds.- Vector Bundles.- Vectors and Covectors.- Differential Forms.- Lie Derivatives.- Lie Groups.- Frobenius Theorem.- Principle Bundles.- Connections on Principle Bundles.- Curvature of a Connection.- Classical Electromagnetism.- Yang-Mills Theory.- Gauge Theory.- The Dirac Monopole.- Instantons.- What Next?.- Discussion of the Exercises.

Details

Erscheinungsjahr:	2015
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Universitext
Inhalt:	xv 280 S. 85 s/w Illustr. 280 p. 85 illus.
ISBN-13:	9783319147642
ISBN-10:	3319147641
Sprache:	Englisch
Herstellernummer:	978-3-319-14764-2
Einband:	Kartoniert / Broschiert
Autor:	Sontz, Stephen Bruce
Hersteller:	Springer Springer International Publishing AG Universitext
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 17 mm
Von/Mit:	Stephen Bruce Sontz
Erscheinungsdatum:	11.05.2015
Gewicht:	0,458 kg