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: Topology, Geometry and Gauge fields
    sub title: Interactions
  name:
    name part: Naber, Gregory L.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 420 p. online resource.
  abstract: This volume is intended to carry on the program, initiated in Topology, Geometry, and Gauge Fields: Foundations (Springer, 2010), of exploring the interrelations between particle physics and topology that arise from their shared notion of a gauge field. The text begins with a synopsis of the geometrical background assumed of the reader (manifolds, Lie groups, bundles, connections, etc.). There follows a lengthy, and somewhat informal discussion of a number of the most basic of the classical gauge theories arising in physics, including classical electromagnetic theory and Dirac monopoles, the Klein-Gordon and Dirac equations and SU(2) Yang-Mills-Higgs theory. The real purpose here is to witness such things as spacetime manifolds, spinor structures, de Rham cohomology, and Chern classes arise of their own accord in meaningful physics. All of these are then developed rigorously in the remaining chapters. With the precise definitions in hand, one can, for example, fully identify magnetic charge and instanton number with the Chern numbers of the bundles on which the charge and instanton live, and uncover the obstruction to the existence of a spinor structure in the form of the second Stiefel-Whitney class. This second edition of the book includes, in an Appendix, a much expanded sketch of Seiberg-Witten gauge theory, including a brief discussion of its origins in physics and its implications for topology. To provide the reader with the opportunity to pause en route and join in the fun, there are 228 exercises, each an integral part of the development and each located at precisely the point at which it can be solved with optimal benefit. Reviews of first edition: “Naber’s goal is not to teach a sterile course on geometry and topology, but rather to enable us to see the subject in action, through gauge theory.” (SIAM Review) “The presentation … is enriched by detailed discussions about the physical interpretations of connections, their curvatures and characteristic classes…
  table of contents: Preface -- Acknowledgements -- Geometrical Background -- Physical Motivation -- Frame Bundles and Spacetime -- Differential Forms and Integration Introduction -- de Rham Cohomology Introduction -- Characteristic Classes -- Appendix -- References -- Symbols -- Index.
  note: by Gregory L. Naber.
  subject:
    topic: Mathematics
  subject:
    topic: Geometry
  subject:
    topic: Combinatorics
  subject:
    topic: Physics
  subject:
    topic: Mathematics
  subject:
    topic: Geometry
  subject:
    topic: Theoretical, Mathematical and Computational Physics
  subject:
    topic: Combinatorics
  classification: QA440-699
  classification: 516
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Applied Mathematical Sciences, 141
  identifier: 9781441978950
  identifier: http://dx.doi.org/10.1007/978-1-4419-7895-0
  record info:
    record creation date: 110321
    record change date: 20151103125630.0
    record identifier: 978-1-4419-7895-0