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: Modern Differential Geometry in Gauge Theories
    sub title: Maxwell Fields, Volume I
  name:
    name part: Mallios, Anastasios.
    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: 2006
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVII, 293 p. online resource.
  abstract: Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications. Modern Differential Geometry in Gauge Theories is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Beginning with Volume 1, the focus is on Maxwell fields. All the basic concepts of this mathematical approach are formulated and used thereafter to describe elementary particles, electromagnetism, and geometric prequantization. Maxwell fields are fully examined and classified in the language of sheaf theory and sheaf cohomology. Continuing in Volume 2, this sheaf-theoretic approach is applied to Yang–Mills fields in general. The text contains a wealth of detailed and rigorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduate students, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity.
  table of contents: Maxwell Fields: General Theory -- The Rudiments of Abstract Differential Geometry -- Elementary Particles: Sheaf-Theoretic Classification, by Spin-Structure, According to Selesnick’s Correspondence Principle -- Electromagnetism -- Cohomological Classification of Maxwell and Hermitian Maxwell Fields -- Geometric Prequantization.
  note: by Anastasios Mallios.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Field theory (Physics)
  subject:
    topic: Global analysis (Mathematics)
  subject:
    topic: Manifolds (Mathematics)
  subject:
    topic: Differential geometry
  subject:
    topic: Physics
  subject:
    topic: Optics
  subject:
    topic: Electrodynamics
  subject:
    topic: Elementary particles (Physics)
  subject:
    topic: Quantum field theory
  subject:
    topic: Mathematics
  subject:
    topic: Differential Geometry
  subject:
    topic: Mathematical Methods in Physics
  subject:
    topic: Field Theory and Polynomials
  subject:
    topic: Elementary Particles, Quantum Field Theory
  subject:
    topic: Optics and Electrodynamics
  subject:
    topic: Global Analysis and Analysis on Manifolds
  classification: QA641-670
  classification: 516.36
  related item:
    title info:
      title: Springer eBooks
  identifier: 9780817644741
  identifier: http://dx.doi.org/10.1007/0-8176-4474-1
  record info:
    record creation date: 100301
    record change date: 20151204174315.0
    record identifier: 978-0-8176-4474-1