Modern Differential Geometry in Gauge Theories
Maxwell Fields, Volume I
Seiten
2005
|
2006 ed.
Birkhauser Boston Inc (Verlag)
978-0-8176-4378-2 (ISBN)
Birkhauser Boston Inc (Verlag)
978-0-8176-4378-2 (ISBN)
Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Using modern differential geometry from the author's perspective, this work describes physical theories of a geometric character without using any notion of calculus (smoothness).
Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications.
Modern Differential Geometry in Gauge Theories is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Beginning with Volume 1, the focus is on Maxwell fields. Continuing in Volume 2, this sheaf-theoretic approach is applied to Yang–Mills fields in general. Thetext contains a wealth of detailed and rigorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduate students, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity.
Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications.
Modern Differential Geometry in Gauge Theories is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Beginning with Volume 1, the focus is on Maxwell fields. Continuing in Volume 2, this sheaf-theoretic approach is applied to Yang–Mills fields in general. Thetext contains a wealth of detailed and rigorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduate students, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity.
Maxwell Fields: General Theory.- The Rudiments of Abstract Differential Geometry.- Elementary Particles: Sheaf-Theoretic Classification, by Spin-Structure, According to Selesnick’s Correspondence Principle.- Electromagnetism.- Cohomological Classification of Maxwell and Hermitian Maxwell Fields.- Geometric Prequantization.
| Reihe/Serie | Maxwell Fields ; Vol.1 | Progress in Mathematical Physics ; Vol.41 |
|---|---|
| Mitarbeit |
Anpassung von: George A. Anastassiou |
| Zusatzinfo | XVII, 293 p. |
| Verlagsort | Secaucus |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| Naturwissenschaften ► Physik / Astronomie | |
| ISBN-10 | 0-8176-4378-8 / 0817643788 |
| ISBN-13 | 978-0-8176-4378-2 / 9780817643782 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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