Local operators in integrable models. I
- Responsibility
- Michio Jimbo, Tetsuji Miwa, Fedor Smirnov
- Publication
- Providence, Rhode Island : American Mathematical Society, [2021]
- Copyright notice
- ©2021
- Physical description
- xii, 192 pages : illustrations ; 26 cm
- Series
- Mathematical surveys and monographs ; no. 256.
At the library
Science Library (Li and Ma)
Stacks
| Call number | Status |
|---|---|
| QA3 .A4 V.256 |
More options
Description
Creators/Contributors
- Author/Creator
- Jimbo, M. (Michio), author.
- Contributor
- Miwa, T. (Tetsuji), author.
- Smirnov, F. A., author.
Contents/Summary
- Bibliography
- Includes bibliographical references (pages 187-190) and index
- Contents
-
- Formulation of the problem Spectral problem in Matsubara direction and quantum groups Ferminions Main theorem Applications and generalisations Quasi-classical limit and algebraic geometry Notation Bibliography Index.
- (source: Nielsen Book Data)
- Summary
-
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. Going through the book, readers will find themselves at the forefront of this rapidly developing research field.
(source: Nielsen Book Data)
Subjects
- Subjects
- Integral equations.
- Operator theory.
- Quantum field theory.
- Statistical mechanics.
- Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics.
- Statistical mechanics, structure of matter -- Equilibrium statistical mechanics -- Exactly solvable models; Bethe ansatz.
- Associative rings and algebras -- Hopf algebras, quantum groups and related topics -- Yang-Baxter equations.
- Nonassociative rings and algebras -- Lie algebras and Lie superalgebras -- Quantum groups (quantized enveloping algebras) and related deformations.
- Quantum theory -- Quantum field theory; related classical field theories -- Two-dimensional field theories, conformal field theories, etc. in quantum mechanics.
- Quantum theory -- Groups and algebras in quantum theory -- Quantum groups and related algebraic methods applied to problems in quantum theory.
Bibliographic information
- Publication date
- 2021
- Copyright date
- 2021
- Series
- Mathematical surveys and monographs, 0076-5376 ; volume 256
- ISBN
- 9781470465520 paperback volume 1
- 1470465523 paperback volume 1
- 9781470465766 electronic book volume 1
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