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Cover: 9781461428381 | Topology, Geometry and Gauge fields | Interactions | Gregory L. Naber
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Topology, Geometry and Gauge fields
Interactions
Taschenbuch von Gregory L. Naber
Sprache: Englisch

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Beschreibung
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. This second edition has replaced a brief appendix in the first on the Seiberg-Witten equations with a much more detailed survey of Donaldson-Witten Theory and the Witten Conjecture regarding the relationship between Donaldson and Seiberg-Witten invariants.
A large number of exercises are included to encourage active participation on the part of the reader.
Review from first edition:
"It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics...Naber combines a knowledge of his subject with an excellent informal writing style."
SIAM REVIEW
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. This second edition has replaced a brief appendix in the first on the Seiberg-Witten equations with a much more detailed survey of Donaldson-Witten Theory and the Witten Conjecture regarding the relationship between Donaldson and Seiberg-Witten invariants.
A large number of exercises are included to encourage active participation on the part of the reader.
Review from first edition:
"It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics...Naber combines a knowledge of his subject with an excellent informal writing style."
SIAM REVIEW
Über den Autor
Gregory L. Naber is a Professor in the Department of Mathematics at Drexel University in Philadelphia, PA.
Zusammenfassung
During the past two decades gauge theory has been the focus of intense mathematical scrutiny. This book, together with the author's earlier book, Topology, Geometry and Gauge Fields: Foundations, Springer 1997, provides a gentle introduction to the basics of the subject with the somewhat unique feature of picking out what students need to know from both the mathematics and physics of the subject. Extensive exercises are included to encourage readers to actively participate in the material.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2013
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Applied Mathematical Sciences
Inhalt: xii
420 S.
ISBN-13: 9781461428381
ISBN-10: 1461428386
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Naber, Gregory L.
Auflage: Softcover reprint of hardcover 2nd ed. 2011
Hersteller: Springer New York
Springer US, New York, N.Y.
Applied Mathematical Sciences
Maße: 235 x 155 x 24 mm
Von/Mit: Gregory L. Naber
Erscheinungsdatum: 19.04.2013
Gewicht: 0,651 kg
Artikel-ID: 105959673
Über den Autor
Gregory L. Naber is a Professor in the Department of Mathematics at Drexel University in Philadelphia, PA.
Zusammenfassung
During the past two decades gauge theory has been the focus of intense mathematical scrutiny. This book, together with the author's earlier book, Topology, Geometry and Gauge Fields: Foundations, Springer 1997, provides a gentle introduction to the basics of the subject with the somewhat unique feature of picking out what students need to know from both the mathematics and physics of the subject. Extensive exercises are included to encourage readers to actively participate in the material.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2013
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Applied Mathematical Sciences
Inhalt: xii
420 S.
ISBN-13: 9781461428381
ISBN-10: 1461428386
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Naber, Gregory L.
Auflage: Softcover reprint of hardcover 2nd ed. 2011
Hersteller: Springer New York
Springer US, New York, N.Y.
Applied Mathematical Sciences
Maße: 235 x 155 x 24 mm
Von/Mit: Gregory L. Naber
Erscheinungsdatum: 19.04.2013
Gewicht: 0,651 kg
Artikel-ID: 105959673
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