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The Resource Topology, geometry and gauge fields : interactions, Gregory L. Naber

Topology, geometry and gauge fields : interactions, Gregory L. Naber

Creator
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)
Language
eng
Work
Publication
Edition
2nd ed.
Extent
1 online resource (xii, 419 pages).
Contents
  • Geometrical background
  • Physical motivation
  • Frame bundles and spacetimes
  • Differential forms and integration
  • De Rham Cohomology
  • Characteristic classes
Isbn
9781441978943
Instance
Label
Topology, geometry and gauge fields : interactions
Title
Topology, geometry and gauge fields
Title remainder
interactions
Statement of responsibility
Gregory L. Naber
Creator
Subject
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
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1948-
http://library.link/vocab/creatorName
Naber, Gregory L.
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
http://library.link/vocab/subjectName
  • Topology
  • Geometry
  • Gauge fields (Physics)
  • Mathematical physics
  • Gauge fields (Physics)
  • Geometry
  • Mathematical physics
  • Topology
Label
Topology, geometry and gauge fields : interactions, Gregory L. Naber
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Geometrical background -- Physical motivation -- Frame bundles and spacetimes -- Differential forms and integration -- De Rham Cohomology -- Characteristic classes
Control code
719363278
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (xii, 419 pages).
Form of item
online
Isbn
9781441978943
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
  • 9781441978943
  • 10.1007/978-1-4419-7
http://library.link/vocab/ext/overdrive/overdriveId
978-1-4419-7894-3
Specific material designation
remote
System control number
(OCoLC)719363278
Label
Topology, geometry and gauge fields : interactions, Gregory L. Naber
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
Geometrical background -- Physical motivation -- Frame bundles and spacetimes -- Differential forms and integration -- De Rham Cohomology -- Characteristic classes
Control code
719363278
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (xii, 419 pages).
Form of item
online
Isbn
9781441978943
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
  • 9781441978943
  • 10.1007/978-1-4419-7
http://library.link/vocab/ext/overdrive/overdriveId
978-1-4419-7894-3
Specific material designation
remote
System control number
(OCoLC)719363278

Subject

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