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Differential geometry and mathematic...

Rudolph, Gerd.

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Differential geometry and mathematical physics.. Part II,. Fibre bundles, topology and gauge fields

Record Type:	Electronic resources : Monograph/item
Title/Author:	Differential geometry and mathematical physics./ by Gerd Rudolph, Matthias Schmidt.
remainder title:	Fibre bundles, topology and gauge fields
Author:	Rudolph, Gerd.
other author:	Schmidt, Matthias.
Published:	Dordrecht :Springer Netherlands : : 2017.,
Description:	xvi, 830 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Geometry, Differential. -
Online resource:	http://dx.doi.org/10.1007/978-94-024-0959-8
ISBN:	9789402409598

Differential geometry and mathematical physics.. Part II,. Fibre bundles, topology and gauge fields
Rudolph, Gerd.

Differential geometry and mathematical physics.Part II,Fibre bundles, topology and gauge fields[electronic resource] /Fibre bundles, topology and gauge fieldsby Gerd Rudolph, Matthias Schmidt. - Dordrecht :Springer Netherlands :2017. - xvi, 830 p. :ill., digital ;24 cm. - Theoretical and mathematical physics,1864-5879. - Theoretical and mathematical physics..

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.

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.

ISBN: 9789402409598

Standard No.: 10.1007/978-94-024-0959-8doiSubjects--Topical Terms:

523835
Geometry, Differential.

LC Class. No.: QC20.7.D52

Dewey Class. No.: 530.15

Differential geometry and mathematical physics.. Part II,. Fibre bundles, topology and gauge fields
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100 1 $a Rudolph, Gerd. $3 3227649
245 1 0 $a Differential geometry and mathematical physics. $n Part II, $p Fibre bundles, topology and gauge fields $h [electronic resource] / $c by Gerd Rudolph, Matthias Schmidt.
246 3 0 $a Fibre bundles, topology and gauge fields
260 $a Dordrecht : $b Springer Netherlands : $b Imprint: Springer, $c 2017.
300 $a xvi, 830 p. : $b ill., digital ; $c 24 cm.
490 1 $a Theoretical and mathematical physics, $x 1864-5879
505 0 $a 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.
520 $a 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.
650 0 $a Geometry, Differential. $3 523835
650 0 $a Mathematical physics. $3 516853
650 0 $a Gauge fields (Physics) $3 524714
650 0 $a Fiber bundles (Mathematics) $3 706076
650 0 $a Topology. $3 522026
650 1 4 $a Physics. $3 516296
650 2 4 $a Mathematical Methods in Physics. $3 890898
650 2 4 $a Differential Geometry. $3 891003
650 2 4 $a Mathematical Physics. $3 1542352
650 2 4 $a Algebraic Geometry. $3 893861
650 2 4 $a Algebraic Topology. $3 891269
650 2 4 $a Elementary Particles, Quantum Field Theory. $3 894026
700 1 $a Schmidt, Matthias. $3 3227650
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Theoretical and mathematical physics. $3 1566264
856 4 0 $u http://dx.doi.org/10.1007/978-94-024-0959-8
950 $a Physics and Astronomy (Springer-11651)