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: Supermathematics and its Applications in Statistical Physics
    sub title: Grassmann Variables and the Method of Supersymmetry
  name:
    name part: Wegner, Franz.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2016
    edition: 1st ed. 2016.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVII, 374 p. 15 illus., 12 illus. in color. online resource.
  abstract: This text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical systems, as well as related topics in statistical physics. Based on many courses and seminars held by the author, one of the pioneers in this field, the reader is given a systematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables is presented in part I. The mathematics of these variables is applied to a random matrix model, path integrals for fermions, dimer models and the Ising model in two dimensions. Supermathematics - the use of commuting and anticommuting variables on an equal footing - is the subject of part II. The properties of supervectors and supermatrices, which contain both commuting and Grassmann components, are treated in great detail, including the derivation of integral theorems. In part III, supersymmetric physical models are considered. While supersymmetry was first introduced in elementary particle physics as exact symmetry between bosons and fermions, the formal introduction of anticommuting spacetime components, can be extended to problems of statistical physics, and, since it connects states with equal energies, has also found its way into quantum mechanics. Several models are considered in the applications, after which the representation of the random matrix model by the nonlinear sigma-model, the determination of the density of states and the level correlation are derived. Eventually, the mobility edge behavior is discussed and a short account of the ten symmetry classes of disorder, two-dimensional disordered models, and superbosonization is given.
  table of contents: Part I Grassmann Variables and Applications -- Part II Supermathematics -- Part III Supersymmetry in Statistical Physics -- Summary and Additional Remarks -- References -- Solutions -- Index.
  note: by Franz Wegner.
  subject:
    topic: Physics
  subject:
    topic: System theory
  subject:
    topic: Mathematical physics
  subject:
    topic: Physics
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Mathematical Physics
  subject:
    topic: Complex Systems
  subject:
    topic: Mathematical Applications in the Physical Sciences
  subject:
    topic: Statistical Physics and Dynamical Systems
  classification: QC5.53
  classification: 530.15
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Physics, 920
  identifier: 9783662491706
  identifier: http://dx.doi.org/10.1007/978-3-662-49170-6
  record info:
    record creation date: 160325
    record change date: 20160927112249.0
    record identifier: 978-3-662-49170-6