Topology, geometry, and gauge fields : interactions
著者
書誌事項
Topology, geometry, and gauge fields : interactions
（Applied mathematical sciences, 141）
Springer, c2011
2nd ed
- : [pbk]
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注記
Includes bibliographical references (p. 401-405) and index
内容説明・目次
内容説明
A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds. The focus of the book is the Yang-Mills-Higgs field and some considerable effort is expended to make clear its origin and significance in physics. Much of the mathematics developed here to study these fields is standard, but the treatment always keeps one eye on the physics and sacrifices generality in favor of clarity. The author brings readers up the level of physics and mathematics needed to conclude with a brief discussion of the Seiberg-Witten invariants. A large number of exercises are included to encourage active participation on the part of the reader.
目次
Preface.- Acknowledgements.- Geometrical Background.- Physical Motivation.- Frame Bundles and Spacetime.- Differential Forms and Integration Introduction.- de Rham Cohomology Introduction.- Characteristic Classes.- Appendix.- References.- Symbols.- Index.
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