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Integrability Using the Sine-Gordon and Thirring Duality : An Introductory Course / Alessandro Torrielli.
- Format:
- Book
- Author/Creator:
- Torrielli, Alessandro, author.
- Series:
- IOP Ebooks Series
- Language:
- English
- Subjects (All):
- Hamiltonian systems.
- Mathematical physics.
- Physical Description:
- 1 online resource (159 pages)
- Edition:
- First edition.
- Place of Publication:
- Bristol, England : IOP Publishing, [2024]
- Summary:
- This book provides a description of the duality between two integrable systems: the 1+1-dimensional Sine-Gordon model and the 1+1-dimensional Thirring model. It's an opportunity for a focussed study of integrability in its wider breadth of interest, maintaining a clear ultimate purpose in mind: understanding the duality between bosons and fermions in 1+1 dimensions.
- Contents:
- Intro
- Acknowledgements
- Author biography
- Alessandro Torrielli
- Chapter Introduction
- 1.1 Prelude
- References
- Chapter Invitation to integrable quantum field theories
- 2.1 Classical integrability
- 2.2 Exact S-matrices
- Chapter The Sine-Gordon model
- 3.1 A very special theory
- 3.2 Classical aspects
- 3.2.1 Solitons
- 3.2.2 Lax pair and classical inverse scattering
- 3.3 Quantum aspects
- 3.3.1 Soliton S-matrix and dressing phase
- 3.4 Breather S-matrix, mixed S-matrix
- 3.5 Sine-Gordon and the XXZ spin-chain
- 3.6 The quantum group Uqsu(2)
- 3.6.1 Towards quantum affine
- 3.6.2 Project
- 3.7 The quantum affine symmetry
- Chapter The Thirring model
- 4.1 Fermions in the game
- 4.2 A small snapshot of the 1 + 1-dimensional particle world
- 4.2.1 Representations for fields
- 4.2.2 Representations for particles
- Chapter 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
- Chapter Remarks on the duality
- 6.1 The paper by Klassen and Melzer
- 6.2 Final remarks
- Chapter Supplement: the residue of the Lee-Yang model
- 7.1 Pole analysis
- Reference
- Chapter Supplement: Hopf algebra properties
- 8.1 Building blocks
- 8.2 Coproducts
- 8.3 R-matrix
- 8.4 RTT relations
- Chapter 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
- Chapter Supplement: the Lieb-Liniger model
- 10.1 The classical theory
- 10.2 Quantisation
- 10.2.1 Direct diagonalisation
- 10.2.2 Integrability method.
- 10.2.3 The spectrum via the algebraic Bethe ansatz
- 10.3 The classical limit
- Chapter Supplement: massless integrability
- 11.1 The limit to zero mass
- 11.2 Massless flows
- 11.2.1 Tricritical to critical Ising
- 11.3 Thermodynamic Bethe ansatz for a simple S-matrix
- Chapter Supplement: a toy model for the Bethe ansatz
- 12.1 Setup
- 12.2 Low N eigenstates
- 12.2.1 N = 2
- 12.2.2 N = 3
- 12.2.3 N&
- #62
- 3
- References.
- Notes:
- Includes bibliographical references.
- Description based on publisher supplied metadata and other sources.
- Description based on print version record.
- Other Format:
- Print version: Torrielli, Alessandro Integrability Using the Sine-Gordon and Thirring Duality
- ISBN:
- 9780750359016
- OCLC:
- 1435947287
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