Research Catalog

Topology, geometry, and gauge fields : foundations

Title
Topology, geometry, and gauge fields : foundations / Gregory L. Naber.
Author
Naber, Gregory L., 1948-
Publication
New York : Springer, ©1997.

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Details

Description
xviii, 396 pages : illustrations; 25 cm.
Summary
This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author's point of view is that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theory of physicists with the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) -connections on S[subscript 4] with instanton number -1.
Series Statement
Texts in applied mathematics ; 25
Uniform Title
Texts in applied mathematics ; 25.
Subject
  • Topology
  • Geometry
  • Gauge fields (Physics)
  • Mathematical physics
  • geometry
  • Algebraïsche topologie
  • Veldentheorie
  • Mathematische fysica
  • Topologie
  • Géométrie
  • Champs de jauge (physique)
  • Physique mathématique
Bibliography (note)
  • Includes bibliographical references (p. [379]-382) and index.
Contents
Physical and geometrical motivation -- 1. Topological spaces -- 2. Homotopy groups -- 3. Principal bundles -- 4. Differentiable manifolds and matrix lie groups -- 5. Gauge fields and instantons -- Appendix: SU(2) and SO(3).
ISBN
  • 0387949461
  • 9780387949468
LCCN
96049166
OCLC
  • ocm36023992
  • 36023992
  • SCSB-868448
Owning Institutions
Princeton University Library