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: Group Representation for Quantum Theory
  name:
    name part: Hayashi, Masahito.
    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: XXVIII, 338 p. 54 illus., 1 illus. in color. online resource.
  abstract: This book explains the group representation theory for quantum theory in the language of quantum theory. As is well known, group representation theory is very strong tool for quantum theory, in particular, angular momentum, hydrogen-type Hamiltonian, spin-orbit interaction, quark model, quantum optics, and quantum information processing including quantum error correction. To describe a big picture of application of representation theory to quantum theory, the book needs to contain the following six topics, permutation group, SU(2) and SU(d), Heisenberg representation, squeezing operation, Discrete Heisenberg representation, and the relation with Fourier transform from a unified viewpoint by including projective representation. Unfortunately, although there are so many good mathematical books for a part of six topics, no book contains all of these topics because they are too segmentalized. Further, some of them are written in an abstract way in mathematical style and, often, the materials are too segmented. At least, the notation is not familiar to people working with quantum theory. Others are good elementary books, but do not deal with topics related to quantum theory. In particular, such elementary books do not cover projective representation, which is more important in quantum theory. On the other hand, there are several books for physicists. However, these books are too simple and lack the detailed discussion. Hence, they are not useful for advanced study even in physics. To resolve this issue, this book starts with the basic mathematics for quantum theory. Then, it introduces the basics of group representation and discusses the case of the finite groups, the symmetric group, e.g. Next, this book discusses Lie group and Lie algebra. This part starts with the basics knowledge, and proceeds to the special groups, e.g., SU(2), SU(1,1), and SU(d). After the special groups, it explains concrete applications to physical systems, e.g., angular momentum, hydrogen-type H…
  table of contents: Foundation of Quantum Theory -- Group Representation -- Representations of Lie Group and Lie Algebra (Basics) -- Representations of Lie Group and Lie Algebra (Special Case) -- Representations of Lie Group and Lie Algebra (General Case) -- Bosonic System -- Discretization of Bosonic System.
  note: by Masahito Hayashi.
  subject:
    topic: Physics
  subject:
    topic: Group theory
  subject:
    topic: Quantum computers
  subject:
    topic: Mathematical physics
  subject:
    topic: Quantum physics
  subject:
    topic: Spintronics
  subject:
    topic: Physics
  subject:
    topic: Quantum Physics
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Quantum Information Technology, Spintronics
  subject:
    topic: Quantum Computing
  subject:
    topic: Mathematical Physics
  classification: QC173.96-174.52
  classification: 530.12
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319449067
  identifier: http://dx.doi.org/10.1007/978-3-319-44906-7
  record info:
    record creation date: 161118
    record change date: 20161118105224.0
    record identifier: 978-3-319-44906-7