UID:
almahu_9947363069702882
Umfang:
XIII, 446 p.
,
online resource.
ISBN:
9781475768503
Serie:
Applied Mathematical Sciences, 141
Inhalt:
This volume is intended to carryon the program initiated in Topology, Geometry, and Gauge Fields: Foundations (henceforth, [N4]). It is written in much the same spirit and with precisely the same philosophical motivation: Mathematics and physics have gone their separate ways for nearly a century now and it is time for this to end. Neither can any longer afford to ignore the problems and insights of the other. Why are Dirac magnetic monopoles in one-to-one correspondence with the principal U(l) bundles over S2? Why do Higgs fields fall into topological types? What led Donaldson, in 1980, to seek in the Yang-Mills equations of physics for the key that unlocks the mysteries of smooth 4-manifolds and what phys ical insights into quantum field theory led Witten, fourteen years later, to propose the vastly simpler, but apparently equivalent Seiberg-Witten equations as an alternative? We do not presume to answer these questions here, but only to promote an atmosphere in which both mathematicians and physicists recognize the need for answers. More succinctly, we shall endeavor to provide an exposition of elementary topology and geometry that keeps one eye on the physics in which our concepts either arose in dependently or have been found to lead to a deeper understanding of the phenomena. Chapter 1 provides a synopsis of the geometrical background we assume of our readers (manifolds, Lie groups, bundles, connections, etc. ).
Anmerkung:
1 Geometrical Background -- 2 Physical Motivation -- 3 Frame Bundles and Spacetimes -- 4 Differential Forms and Integration -- 5 de Rham Cohomology -- 6 Characteristic Classes -- References -- Symbols.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9781475768527
Sprache:
Englisch
DOI:
10.1007/978-1-4757-6850-3
URL:
http://dx.doi.org/10.1007/978-1-4757-6850-3
URL:
Volltext
(lizenzpflichtig)
