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

Format:

Book

Author/Creator:

Torrielli, Alessandro, author.

Contributor:

Institute of Physics (Great Britain), publisher.

Series:

IOP (Series). Release 24.

IOP ebooks. 2024 collection.

[IOP release $release]

IOP ebooks. [2024 collection]

Language:

English

Subjects (All):

Hamiltonian systems.

Mathematical physics.

Physical Description:

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

Place of Publication:

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2024]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

Biography/History:

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.

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.

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

12. Supplement : a toy model for the Bethe ansatz

12.1. Setup

12.2. Low N eigenstates.

Notes:

"Version: 20240501"--Title page verso.

Includes bibliographical references.

Title from PDF title page (viewed on June 1, 2024).

Other Format:

Print version:

ISBN:

9780750358996

9780750358989

OCLC:

1435947287

Access Restriction:

Restricted for use by site license.