Yang-Baxter equation and quantum enveloping algebras
著者
書誌事項
Yang-Baxter equation and quantum enveloping algebras
（Advanced series on theoretical physical science, v. 1）
World Scientific, c1993
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注記
"Institute of Theoretical Physics, Beijing"
Bibliography: p. 302-314
Includes index
内容説明・目次
内容説明
The exact solution of C N Yang's one-dimensional many-body problem with repulsive delta-function interactions and R J Baxter's eight-vertex statistical model are brilliant achievements in many-body statistical physics. A nonlinear equation, now known as the Yang-Baxter equation, is the key to the solution of both problems. The Yang-Baxter equation has also come to play an important role in such diverse topics as completely integrable statistical models, conformal and topological field theories, knots and links, braid groups and quantum enveloping algebras.This pioneering textbook attempts to make accessible results in this rapidly-growing area of research. The author presents the mathematical fundamentals at the outset, then develops an intuitive understanding of Hopf algebras, quantisation of Lie bialgebras and quantum enveloping algebras. The historical derivation of the Yang-Baxter equation from statistical models is recounted, and the interpretation and solution of the equation are systematically discussed. Throughout, emphasis is placed on acquiring calculation skills through physical understanding rather than achieving mathematical rigour.Originating from the author's own research experience and lectures, this book will prove both an excellent graduate text and a useful work of reference.
目次
- Mathematical preliminaries
- origin of the Yang-Baxter equation
- classical Yang-Baxter equation
- quantum enveloping algebras
- quantum Clebsch-Gordan co-efficients
- simple Yang-Baxter equation
- trigonometric and rational solutions
- non-generic q values.
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