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Topology, geometry, and gauge fields : foundations / Gregory L. Naber.

By: Series: Texts in applied mathematics ; 25.New York : Springer, �1997Description: xviii, 396 pages : illustrations ; 25 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 0387949461
  • 9780387949468
Subject(s): DDC classification:
  • 516.3/62 21
LOC classification:
  • QC20.7.T65 N33 1997
Other classification:
  • 33.06
Online resources:
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).
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.
Holdings
Item type Current library Call number Copy number Status Date due Barcode Item holds
BOOK BOOK NCAR Library Foothills Lab QC20.7 .T65 .N33 1997 1 Available 50583020022137
Total holds: 0

Includes bibliographical references (pages 379-382) and index.

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.

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).

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