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Title
Differential geometry and mathematical physics. Part II, Fibre bundles, topology and gauge fields / Gerd Rudolph, Matthias Schmidt.
ISBN
9789402409598 (electronic book)
9402409599 (electronic book)
9789402409581
Published
Dordrecht, the Netherlands : Springer, 2017.
Language
English
Description
1 online resource.
Item Number
10.1007/978-94-024-0959-8 doi
Call Number
QC20.7.D52
Dewey Decimal Classification
530.15
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Vendor-supplied metadata.
Series
Theoretical and mathematical physics (Springer (Firm))
Available in Other Form
Print version: 9789402409581
Fibre bundles and connections
Linear connections and Riemannian geometry
Homotopy theory of principal fibre bundles. Classification
Cohomology theory of fibre bundles. Characteristic classes
Clifford algebras, spin structures and Dirac operators
The Yang-Mills equation
Matter fields and model building
The gauge orbit space
Elements of quantum gauge theory
A Field restriction and field extension
B The Conformal Group of the 4-sphere
C Simple Lie algebras. Root diagrams
D z -function regularization
E K-theory and index bundles
F Determinant line bundles
G Eilenberg-MacLane spaces
References. Index.
