rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Differential Geometry and Mathematical Physics
    sub title: Part II. Fibre Bundles, Topology and Gauge Fields
  name:
    name part: Rudolph, Gerd.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Schmidt, Matthias.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: ne
    date issued: 2017
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 830 p. 15 illus., 2 illus. in color. online resource.
  abstract: 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.
  table of 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 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.
  note: by Gerd Rudolph, Matthias Schmidt.
  subject:
    topic: Physics
  subject:
    topic: Algebraic geometry
  subject:
    topic: Differential geometry
  subject:
    topic: Algebraic topology
  subject:
    topic: Mathematical physics
  subject:
    topic: Elementary particles (Physics)
  subject:
    topic: Quantum field theory
  subject:
    topic: Physics
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Differential Geometry
  subject:
    topic: Mathematical Physics
  subject:
    topic: Algebraic Geometry
  subject:
    topic: Algebraic Topology
  subject:
    topic: Elementary Particles, Quantum Field Theory
  classification: QC5.53
  classification: 530.15
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Theoretical and Mathematical Physics
  identifier: 9789402409598
  identifier: http://dx.doi.org/10.1007/978-94-024-0959-8
  record info:
    record creation date: 170322
    record change date: 20170322071919.0
    record identifier: 978-94-024-0959-8