TY  - BOOK
AU  - Torrielli,Alessandro
ED  - Institute of Physics (Great Britain),
TI  - Integrability using the Sine-Gordon and Thirring duality: an introductory course 
T2  - [IOP release $release]
SN  - 9780750358996
AV  - QA614.83 .T675 2024eb
PY  - 2024///]
CY  - Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK)
PB  - IOP Publishing
KW  - Hamiltonian systems
KW  - Mathematical physics
KW  - bicssc
KW  - SCIENCE / Physics / Mathematical & Computational
KW  - bisacsh
N1  - "Version: 20240501"--Title page verso; Includes bibliographical references; 1. Introduction -- 1.1. Prelude; 2. Invitation to integrable quantum field theories -- 2.1. Classical integrability -- 2.2. Exact S-matrices; 3. The sine-Gordon model -- 3.1. A very special theory -- 3.2. Classical aspects -- 3.3. Quantum aspects -- 3.4. Breather S-matrix, mixed S-matrix -- 3.5. Sine-Gordon and the XXZ spin-chain -- 3.6. The quantum group Uq(su(2)) -- 3.7. The quantum affine symmetry; 4. The Thirring model -- 4.1. Fermions in the game -- 4.2. A small snapshot of the 1 + 1-dimensional particle world; 5. Duality between sine-Gordon and Thirring -- 5.1. Coleman's argument -- 5.2. Project -- 5.3. Mandelstam's construction -- 5.4. Bethe ansatz -- 5.5. Form factors; 6. Remarks on the duality -- 6.1. The paper by Klassen and Melzer -- 6.2. Final remarks; 7. Supplement : the residue of the Lee-Yang model -- 7.1. Pole analysis; 8. Supplement : Hopf algebra properties -- 8.1. Building blocks -- 8.2. Coproducts -- 8.3. R-matrix -- 8.4. RTT relations; 9. Supplement : Yangians -- 9.1. Drinfeld's first realisation -- 9.2. Drinfeld's second realisation -- 9.3. Universal R-matrix of the Yangian of su(2) -- 9.4. Principal chiral model -- 9.5. More on the quantum-classical transition; 10. Supplement : the Lieb-Liniger model -- 10.1. The classical theory -- 10.2. Quantisation; 11. Supplement : massless integrability -- 11.1. The limit to zero mass -- 11.2. Massless flows -- 11.3. Thermodynamic Bethe ansatz for a simple S-matrix; 12. Supplement : a toy model for the Bethe ansatz -- 12.1. Setup -- 12.2. Low N eigenstates; Full-text restricted to subscribers or individual document purchasers; Professional and scholarly; Also available in print
N2  - This book provides a detailed description of the duality between two integrable systems: the 1+1-dimensional sine-Gordon model and the 1+1-dimensional Thirring model. While of great importance per se, this duality is only part of the target of the book. In order to reach an understanding of the subtleties involved in the duality, one has to take a journey through the properties of quantum integrable systems, building from the ground up the theory of exact S-matrices and familiarising oneself with the mathematical concept of a quantum group. The book therefore becomes an opportunity for a focussed study of integrability in its wider breadth of interest, always maintaining a clear ultimate purpose in mind: understanding the duality between bosons and fermions in 1+1 dimensions. This should make going through the book from the point of view of the reader/early-career researcher a live enterprise, as opposed to a more passive learning exercise
UR  - https://iopscience.iop.org/book/mono/978-0-7503-5899-6
ER  -