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

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"Version: 20240501"--Title page verso.Includes bibliographical references.1. Introduction -- 1.1. Prelude2. Invitation to integrable quantum field theories -- 2.1. Classical integrability -- 2.2. Exact S-matrices3. 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 symmetry4. The Thirring model -- 4.1. Fermions in the game -- 4.2. A small snapshot of the 1 + 1-dimensional particle world5. 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 factors6. Remarks on the duality -- 6.1. The paper by Klassen and Melzer -- 6.2. Final remarks7. Supplement : the residue of the Lee-Yang model -- 7.1. Pole analysis8. Supplement : Hopf algebra properties -- 8.1. Building blocks -- 8.2. Coproducts -- 8.3. R-matrix -- 8.4. RTT relations9. 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 transition10. Supplement : the Lieb-Liniger model -- 10.1. The classical theory -- 10.2. Quantisation11. Supplement : massless integrability -- 11.1. The limit to zero mass -- 11.2. Massless flows -- 11.3. Thermodynamic Bethe ansatz for a simple S-matrix12. 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.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.Professional and scholarly.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.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.Title from PDF title page (viewed on June 1, 2024).

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: .,

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1 online resource (various pagings) :illustrations (some color).

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English

ISBN/ISSN

9780750358996

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515/.39

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Subject(s)

SCIENCE / Physics / Mathematical & Computational.
Mathematical physics.
Hamiltonian systems.

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Alessandro Torrielli.

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