The Resource Differential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields, by Gerd Rudolph, Matthias Schmidt, (electronic resource)
Differential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields, by Gerd Rudolph, Matthias Schmidt, (electronic resource)
 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, Hstructures and the Postnikov approximation of classifying spaces. Given the great importance of Dirac operators in gauge theory, a complete proof of the AtiyahSinger Index Theorem is presented. The gauge theory part contains the study of YangMills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the SeibergWitten 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 nongeneric 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
 Language
 eng
 Extent
 XVI, 830 p. 15 illus., 2 illus. in color.
 Contents

 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 YangMills 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 4sphere
 C Simple Lie algebras. Root diagrams
 D z function regularization
 E Ktheory and index bundles
 F Determinant line bundles
 G EilenbergMacLane spaces
 References. Index
 Isbn
 9789402409598
 Label
 Differential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields
 Title
 Differential Geometry and Mathematical Physics
 Title remainder
 Part II. Fibre Bundles, Topology and Gauge Fields
 Statement of responsibility
 by Gerd Rudolph, Matthias Schmidt
 Language
 eng
 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, Hstructures and the Postnikov approximation of classifying spaces. Given the great importance of Dirac operators in gauge theory, a complete proof of the AtiyahSinger Index Theorem is presented. The gauge theory part contains the study of YangMills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the SeibergWitten 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 nongeneric 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
 Image bit depth
 0
 Literary form
 non fiction
 Series statement
 Theoretical and Mathematical Physics,
 Label
 Differential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields, by Gerd Rudolph, Matthias Schmidt, (electronic resource)
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 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
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 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 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 YangMills 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 4sphere  C Simple Lie algebras. Root diagrams  D z function regularization  E Ktheory and index bundles  F Determinant line bundles  G EilenbergMacLane spaces  References. Index
 http://library.link/vocab/cover_art
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 http://library.link/vocab/discovery_link
 {'f': 'http://opac.lib.rpi.edu/record=b4257955'}
 Extent
 XVI, 830 p. 15 illus., 2 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9789402409598
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other physical details
 online resource.
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 absent
 Reformatting quality
 access
 Specific material designation
 remote
Subject
 Algebraic Geometry
 Algebraic Topology
 Algebraic topology
 Differential Geometry
 Elementary Particles, Quantum Field Theory
 Geometry, Algebraic
 Geometry, Differential
 Mathematical Methods in Physics
 Mathematical Physics
 Mathematical physics
 Particles (Nuclear physics)
 Physics
 Quantum field theory
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.rpi.edu/portal/DifferentialGeometryandMathematicalPhysics/FisJMn9vrIQ/" typeof="WorkExample http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.rpi.edu/portal/DifferentialGeometryandMathematicalPhysics/FisJMn9vrIQ/">Differential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields, by Gerd Rudolph, Matthias Schmidt, (electronic resource)</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.lib.rpi.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.rpi.edu/">Rensselaer Libraries</a></span></span></span></span></div>