Local Operators in Integrable Models I (Mathematical Surveys and Monographs, 256)

Michio Jimbo, Tetsuji Miwa, Fedor Smirnov

ISBN 10: 1470465523 / ISBN 13: 9781470465520

Published by American Mathematical Society, 2021

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Bibliographic Details

• Title: Local Operators in Integrable Models I (Mathematical Surveys and Monographs, 256)
• Publisher: American Mathematical Society
• Publication Date: 2021
• Language: English
• ISBN 10: 1470465523
• ISBN 13: 9781470465520
• Binding: paperback
• Condition: New
• Book Type: book

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Synopsis

Integrable models in statistical mechanics and quantum field theory constitute a rich research field at the crossroads of modern mathematics and theoretical physics. An important issue to understand is the space of local operators in the system and, ultimately, their correlation functions and form factors. This book is the first published monograph on this subject. It treats integrable lattice models, notably the six\-vertex model and the XXZ Heisenberg spin chain. A pair of fermions is introduced and used to create a basis of the space of local operators, leading to the result that all correlation functions at finite distances are expressible in terms of two transcendental functions with rational coefficients. Step\-by\-step explanations are given for all materials necessary for this construction, ranging from algebraic Bethe ansatz, representations of quantum groups, and the Bazhanov\-Lukyanov\-Zamolodchikov construction in conformal field theory to Riemann surfaces and their Jacobians. Several examples and applications are given along with numerical results.\n\nGoing through the book, readers will find themselves at the forefront of this rapidly developing research field.

About the Author

Michio Jimbo: Rikkyo University, Tokyo, Japan, Tetsuji Miwa: Kyoto University, Kyoto, Japan, Fedor Smirnov: CNRS, Paris, France