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:
    non sort: The
    title: c and a-Theorems and the Local Renormalisation Group
  name:
    name part: Shore, Graham.
    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: 2017
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VII, 102 p. 5 illus., 3 illus. in color. online resource.
  abstract: The Zamolodchikov c-theorem has led to important new insights in the understanding of the Renormalisation Group (RG) and the geometry of the space of QFTs. The present primer introduces and reviews the parallel developments of the search for a higher-dimensional generalisation of the c-theorem and of the Local RG (LRG). The idea of renormalisation with position-dependent couplings, running under local Weyl scaling, is traced from its early realisations to the elegant modern formalism of the LRG. The key rôle of the associated Weyl consistency conditions in establishing RG flow equations for the coefficients of the trace anomaly in curved spacetime, and their relation to the c-theorem and four-dimensional a-theorem, is explained in detail. A number of different derivations of the c-theorem in two dimensions are presented and subsequently generalised to four dimensions. The obstructions to establishing monotonic C-functions related to the trace anomaly coefficients in four dimensions are explained. The possibility of deriving an a-theorem for the coefficient of the Euler-Gauss-Bonnet density is explored, initially by formulating the QFT on maximally symmetric spaces. Then the formulation of the weak a-theorem using a dispersion relation for four-point functions is presented. Finally, the application of the LRG to the issue of limit cycles in theories with a global symmetry is described, shedding new light on the geometry of the space of couplings in QFT.
  table of contents: Introduction -- Renormalisation and the Conformal Anomaly -- The Local Renormalisation Group and Weyl Consistency Conditions -- c-Theorem in Two Dimensions -- Local RGE and Weyl Consistency Conditions in Four Dimensions -- c, b and a-Theorems in Four Dimensions -- Global Symmetries and Limit Cycles -- Summary and Outlook.
  note: by Graham Shore.
  subject:
    topic: Physics
  subject:
    topic: Mathematical physics
  subject:
    topic: Quantum field theory
  subject:
    topic: String theory
  subject:
    topic: Physics
  subject:
    topic: Quantum Field Theories, String Theory
  subject:
    topic: Mathematical Physics
  subject:
    topic: Mathematical Methods in Physics
  classification: QC174.45-174.52
  classification: 530.14
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Physics
  identifier: 9783319540009
  identifier: http://dx.doi.org/10.1007/978-3-319-54000-9
  record info:
    record creation date: 170331
    record change date: 20170331082156.0
    record identifier: 978-3-319-54000-9