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Integrability using the Sine-Gordon and Thirring duality : an introductory course / Alessandro Torrielli

Author
Torrielli, Alessandro
Published
Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2024]
Physical Description
1 online resource (various pagings) : illustrations (some color).
Additional Creators
Institute of Physics (Great Britain)
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Full-text restricted to subscribers or individual document purchasers.
Contents
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, and 12. Supplement : a toy model for the Bethe ansatz -- 12.1. Setup -- 12.2. Low N eigenstates.
Summary
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.
Subject(s)
ISBN
9780750358996 ebook
9780750358989 mobi
9780750358972 print
9780750359009 myPrint
Audience Notes
Professional and scholarly.
Note
"Version: 20240501"--Title page verso.
Bibliography Note
Includes bibliographical references.
Other Forms
Also available in print.
Technical Details
Mode of access: World Wide Web.
System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.
Biographical or Historical Sketch
Alessandro Torrielli has been a member of staff at the University of Surrey since 2011, and appointed as Professor of Mathematics in 2022. He graduated with a 110/110 laurea (equivalent to MSc) in Physics from Genoa University, undertook his PhD in Physics from Padua University, then held postdoctoral positions at Padua University, the Humboldt University of Berlin, the Massachusetts Institute of Technology MIT, Utrecht University and York University. His work focuses on algebraic aspects of integrable systems, in particular supersymmetric models of the type appearing in the AdS/CFT correspondence. His research papers have gathered 3867 citations to this day, and his current h-index is 30.
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