Topology for physicists
著者
書誌事項
Topology for physicists
（Die Grundlehren der mathematischen Wissenschaften, 308）
Springer, 1996
Corrected 2nd printing
- : gw
- タイトル別名
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Квантвая теория поля и топология
Kvantovai︠a︡ teorii︠a︡ poli︠a︡ i topologii︠a︡
Quantum field theory and topology
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注記
"An expanded version of the last third of the Russian edition. The remaining content was published in English in 1993, in the same siries, under the title: Quantum field theory and topology"--T.p. verso
Includes bibliography (p. [287]) and indexes
Originally published: Nauka, Moscow, 1989
内容説明・目次
内容説明
In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa tions of motion (solitons and instantons) allow the physicist to leave the frame work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds.
目次
0 Background.- 1 Fundamental Concepts.- 2 The Degree of a Map.- 3 The Fundamental Group and Covering Spaces.- 4 Manifolds.- 5 Differential Forms and Homology in Euclidean Space.- 6 Homology and Cohomology.- 7 Homotopy Classification of Maps of the Sphere.- 8 Homotopy Groups.- 9 Fibered Spaces.- 10 Fibrations and Homotopy Groups.- 11 Homotopy Theory of Fibrations.- 12 Lie Groups.- 13 Lie Algebras.- 14 Topology of Lie Groups and Homogeneous Manifolds.- 15 Geometry of Gauge Fields.- Index of Notation.
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