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Theoretical and Mathematical Physics

Differential Geometry and Mathematical Physics

Part II. Fibre Bundles, Topology and Gauge Fields

Autoren: Rudolph, Gerd, Schmidt, Matthias

  • Offers a rigorous study of the geometric structure of gauge theories
  • Provides a systematic and exhaustive presentation of Dirac operators
  • Enriched by an introduction with interesting historical remarks, a very extensive bibliography, and convenient appendices
Weitere Vorteile

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eBook 130,89 €
Preis für Deutschland (Brutto)
  • ISBN 978-94-024-0959-8
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF, EPUB
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  • Sofortiger eBook Download nach Kauf
Hardcover 174,40 €
Preis für Deutschland (Brutto)
  • ISBN 978-94-024-0958-1
  • Kostenfreier Versand für Individualkunden weltweit
  • Gewöhnlich versandfertig in 3-5 Werktagen.
Über dieses Buch

The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:- Geometry and topology of fibre bundles,- Clifford algebras, spin structures and Dirac operators,- Gauge theory.Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory.The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces.Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory.The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level.

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“Part II of Differential Geometry and Mathematical Physics is a very important pedagogical contribution and a worthy complement to Part I. It presents fine scholarship at a high level, presented clearly and thoroughly, and teaches the reader a great deal of hugely important differential geometry as it informs physics (and that covers a titanic proportion of both fields). Additionally, Gerd Rudolph and Matthias Schmidt do a fabulous job presenting physics is a manner that mathematicians will not find unheimlich. Ausgezeichnet.” (Michael Berg, MAA Reviews, maa.org, May, 2017)

“This book is the second part of a two-volume series on differential geometry and mathematical physics. … The book is addressed to scholars and researchers in differential geometry and mathematical physics, as well as to advanced graduate students who have studied the material covered in the first part of the series. The reader will benefit from remarks and examples in the text, and from the substantial number of exercises at the end of each section.” (Pascal Philip, zbMATH 1364.53001, 2017)


Inhaltsverzeichnis (9 Kapitel)

  • Fibre Bundles and Connections

    Rudolph, Gerd (et al.)

    Seiten 1-92

  • Linear Connections and Riemannian Geometry

    Rudolph, Gerd (et al.)

    Seiten 93-188

  • Homotopy Theory of Principal Fibre Bundles. Classification

    Rudolph, Gerd (et al.)

    Seiten 189-255

  • Cohomology Theory of Fibre Bundles. Characteristic Classes

    Rudolph, Gerd (et al.)

    Seiten 257-352

  • Clifford Algebras, Spin Structures and Dirac Operators

    Rudolph, Gerd (et al.)

    Seiten 353-460

Dieses Buch kaufen

eBook 130,89 €
Preis für Deutschland (Brutto)
  • ISBN 978-94-024-0959-8
  • Versehen mit digitalem Wasserzeichen, DRM-frei
  • Erhältliche Formate: PDF, EPUB
  • eBooks sind auf allen Endgeräten nutzbar
  • Sofortiger eBook Download nach Kauf
Hardcover 174,40 €
Preis für Deutschland (Brutto)
  • ISBN 978-94-024-0958-1
  • Kostenfreier Versand für Individualkunden weltweit
  • Gewöhnlich versandfertig in 3-5 Werktagen.
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Bibliografische Information

Bibliographic Information
Buchtitel
Differential Geometry and Mathematical Physics
Buchuntertitel
Part II. Fibre Bundles, Topology and Gauge Fields
Autoren
Titel der Buchreihe
Theoretical and Mathematical Physics
Copyright
2017
Verlag
Springer Netherlands
Copyright Inhaber
The Editor(s) (if applicable) and The Author(s) 2018
eBook ISBN
978-94-024-0959-8
DOI
10.1007/978-94-024-0959-8
Hardcover ISBN
978-94-024-0958-1
Buchreihen ISSN
1864-5879
Auflage
1
Seitenzahl
XVI, 830
Anzahl der Bilder und Tabellen
13 schwarz-weiß Abbildungen, 2 Abbildungen in Farbe
Themen