Algebraic analysis of solvable lattice models
著者
書誌事項
Algebraic analysis of solvable lattice models
（Regional conference series in mathematics, no. 85）
American Mathematical Society, 1999, c1995
Reprinted with corrections
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注記
Includes bibliographical references (p. 151-162)
At head of title: Conference Board of the Mathematical Sciences, CBMS
"Expository lectures from the NSF-CBMS Regional Conference held at North Carolina State University, Raleigh, North Carolina, June 1-5, 1993" -- T.p. verso
内容説明・目次
内容説明
Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin $1/2$ XXZ chain and the six-vertex model.The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the $XXX$ model is briefly discussed, and the book closes with a discussion of other types of models and related works.
目次
Background of the problem The spin $1/2$ XXZ model for $\Delta <-1$ The six-vertex model in the anti-ferroelectric regime Solvability and symmetry Correlation functions-physical derivation Level one modules and bosonization Vertex operators Space of states-mathematical picture Traces of vertex operators Correlation functions and form factors The $XXX$ limit $q\rightarrow-1$ Discussions List of formulas.
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