05574nam a2200709 i 45000010014000000030004000140050017000180060019000350070015000540080041000690200025001100200024001350200025001590200027001840240035002110350025002460350022002710400040002930500027003330720016003600720023003761000036003992450112004352640098005473000071006453360021007163370026007373380032007634900027007954900034008225000043008565040041008995050036009405050112009765050266010885050120013545050167014745050092016415050076017335050126018095050235019355050096021705050158022665050097024245060075025215200959025965210032035555300029035875380036036165380078036525450703037305880056044336500025044896500026045146500034045406500063045747100054046377760049046918300031047408300034047718560059048059780750358996IOP20251030124832.0m    eo  d        cr cn |||m|||a240601s2024    enka   fob    000 0 eng d  a9780750358996qebook  a9780750358989qmobi  z9780750358972qprint  z9780750359009qmyPrint7 a10.1088/978-0-7503-5899-62doi  a(CaBNVSL)thg00083944  a(OCoLC)1435947287  aCaBNVSLbengerdacCaBNVSLdCaBNVSL 4aQA614.83b.T675 2024eb 7aPHU2bicssc 7aSCI0400002bisacsh1 aTorrielli, Alessandro,eauthor.1 aIntegrability using the Sine-Gordon and Thirring duality :ban introductory course /cAlessandro Torrielli. 1aBristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) :bIOP Publishing,c[2024]  a1 online resource (various pagings) :billustrations (some color).  atext2rdacontent  aelectronic2isbdmedia  aonline resource2rdacarrier1 a[IOP release $release]1 aIOP ebooks. [2024 collection]  a"Version: 20240501"--Title page verso.  aIncludes bibliographical references.  a1. Introduction -- 1.1. Prelude8 a2. Invitation to integrable quantum field theories -- 2.1. Classical integrability -- 2.2. Exact S-matrices8 a3. 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 symmetry8 a4. The Thirring model -- 4.1. Fermions in the game -- 4.2. A small snapshot of the 1 + 1-dimensional particle world8 a5. 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 factors8 a6. Remarks on the duality -- 6.1. The paper by Klassen and Melzer -- 6.2. Final remarks8 a7. Supplement : the residue of the Lee-Yang model -- 7.1. Pole analysis8 a8. Supplement : Hopf algebra properties -- 8.1. Building blocks -- 8.2. Coproducts -- 8.3. R-matrix -- 8.4. RTT relations8 a9. 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 transition8 a10. Supplement : the Lieb-Liniger model -- 10.1. The classical theory -- 10.2. Quantisation8 a11. Supplement : massless integrability -- 11.1. The limit to zero mass -- 11.2. Massless flows -- 11.3. Thermodynamic Bethe ansatz for a simple S-matrix8 a12. Supplement : a toy model for the Bethe ansatz -- 12.1. Setup -- 12.2. Low N eigenstates.  aFull-text restricted to subscribers or individual document purchasers.3 aThis 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.  aProfessional and scholarly.  aAlso available in print.  aMode of access: World Wide Web.  aSystem requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.  aAlessandro 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.  aTitle from PDF title page (viewed on June 1, 2024).  aHamiltonian systems.  aMathematical physics. 7aMathematical physics.2bicssc 7aSCIENCE / Physics / Mathematical & Computational.2bisacsh2 aInstitute of Physics (Great Britain),epublisher. 8iPrint version:z9780750358972z9780750359009 0aIOP (Series).pRelease 24.  aIOP ebooks.p2024 collection.4 uhttps://iopscience.iop.org/book/mono/978-0-7503-5899-6