Algebraic Analysis of Solvable Lattice Models (Cbms Regional Conference Series in Mathematics) - Michio Jimbo, Tetsuji Miwa, Miwa, T (1995)
ISBN 0821803204
Subject Lattice dynamics; Statistical mechanics; Lie algebras; Quantum field theory; Mathematical physics
Publisher American Mathematical Society
Publication Date March 1995
Format Paperback (250 x 176 mm)
Language e
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.
Personal Details
Collection Status In Collection
Index 287
Read It Yes
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Product Details
LoC Classification QC176.8.L3J56 1995
Dewey 530.4/11
Cover Price $21.00
No. of Pages 152