Topology, geometry and gauge fields : interactions

Resource Information

The work Topology, geometry and gauge fields : interactions represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.

Label

Topology, geometry and gauge fields : interactions

Title remainder

interactions

Statement of responsibility

Gregory L. Naber

Creator

• Naber, Gregory L., 1948-

Subject

• Gauge fields (Physics)
• Gauge fields (Physics)
• Geometry
• Geometry
• Geometry
• Mathematical physics
• Mathematical physics
• Mathematical physics
• Topology
• Topology
• Topology
• Gauge fields (Physics)

Language

eng

Summary

This volume is intended to carry on the program, initiated in Topology, Geometry, and Gauge Fields: Foundations (Springer, 2010), of exploring the interrelations between particle physics and topology that arise from their shared notion of a gauge field. The text begins with a synopsis of the geometrical background assumed of the reader (manifolds, Lie groups, bundles, connections, etc.). There follows a lengthy, and somewhat informal discussion of a number of the most basic of the classical gauge theories arising in physics, including classical electromagnetic theory and Dirac monopoles, the Klein-Gordon and Dirac equations and SU(2) Yang-Mills-Higgs theory. The real purpose here is to witness such things as spacetime manifolds, spinor structures, de Rham cohomology, and Chern classes arise of their own accord in meaningful physics. All of these are then developed rigorously in the remaining chapters. With the precise definitions in hand, one can, for example, fully identify magnetic charge and instanton number with the Chern numbers of the bundles on which the charge and instanton live, and uncover the obstruction to the existence of a spinor structure in the form of the second Stiefel-Whitney class. This second edition of the book includes, in an Appendix, a much expanded sketch of Seiberg-Witten gauge theory, including a brief discussion of its origins in physics and its implications for topology. To provide the reader with the opportunity to pause en route and join in the fun, there are 228 exercises, each an integral part of the development and each located at precisely the point at which it can be solved with optimal benefit. Reviews of first edition: "Naber's goal is not to teach a sterile course on geometry and topology, but rather to enable us to see the subject in action, through gauge theory." (SIAM Review) "The presentation ... is enriched by detailed discussions about the physical interpretations of connections, their curvatures and characteristic classes. I particularly enjoyed Chapter 2 where many fundamental physical examples are discussed at great length in a reader friendly fashion. No detail is left to the reader's imagination or interpretation. I am not aware of another source where these very important examples and ideas are presented at a level accessible to beginners." (Mathematical Reviews)

Member of

• Applied mathematical sciences (Springer-Verlag New York Inc.), v. 141

Cataloging source

GW5XE

Dewey number

530.15

Index

index present

LC call number

QC20.7.T65

LC item number

N33 2011

Literary form

non fiction

Nature of contents

• dictionaries
• bibliography

Series statement

Applied mathematical sciences

Series volume

v. 141