Classical Integrability
- O. Babelon, D. Bernard and M. Talon, “Introduction to classical integrable systems,” Cambridge University Press, 2003.
- L. D. Faddeev and L. A. Takhtajan, “Hamiltonian Methods in the Theory of Solitons,” Berlin: Springer (1987)
- S. Novikov, S. V. Manakov, L. P. Pitaevsky and V. E. Zakharov, “Theory Of Solitons. The Inverse Scattering Method,” New York, Usa: Consultants Bureau (1984) 276 P. (Contemporary Soviet Mathematics)
- M.J. Ablowitz, P.A. Clarkson , “Solitons, nonlinear evolution equations and inverse scattering”, Lond.Math.Soc.Lect.Note Ser. 149 .
- O. Babelon, D. Bernard and M. Talon, “Introduction to classical integrable systems,” Cambridge University Press, 2003.
- L. D. Faddeev and L. A. Takhtajan, “Hamiltonian Methods in the Theory of Solitons,” Berlin: Springer (1987)
- S. Novikov, S. V. Manakov, L. P. Pitaevsky and V. E. Zakharov, “Theory Of Solitons. The Inverse Scattering Method,” New York, Usa: Consultants Bureau (1984) 276 P. (Contemporary Soviet Mathematics)
- M.J. Ablowitz, P.A. Clarkson , “Solitons, nonlinear evolution equations and inverse scattering”, Lond.Math.Soc.Lect.Note Ser. 149 .
Quantum inverse scattering method
- Korepin, Bogoliubov, Izergin, “Quantum inverse scattering method and correlation functions”, Cambridge University Press.
- C. Gomez, M. Ruiz-Altaba, G. Sierra , "Quantum Groups in Two-dimensional Physics", Cambridge University Press.
- Korepin, Bogoliubov, Izergin, “Quantum inverse scattering method and correlation functions”, Cambridge University Press.
- C. Gomez, M. Ruiz-Altaba, G. Sierra , "Quantum Groups in Two-dimensional Physics", Cambridge University Press.
Bethe Ansatz
- L.D.Faddeev, “How algebraic Bethe ansatz works for integrable model”, https://arxiv.org/abs/hep-th/9605187.
- Elliott H. Lieb and Werner Liniger "Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State", Phys. Rev. 130, 1605
- L.D.Faddeev, “How algebraic Bethe ansatz works for integrable model”, https://arxiv.org/abs/hep-th/9605187.
- Elliott H. Lieb and Werner Liniger "Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State", Phys. Rev. 130, 1605
TBA
- Al. B. Zamolodchikov, ”Thermodynamic Bethe ansatz in relativistic models: Scaling 3-state potts and Lee-Yang models” Nuclear Physics B, Volume 342, Issue 3, 8 October 1990, Pages 695-720
- Al. B. Zamolodchikov, ”Thermodynamic Bethe ansatz in relativistic models: Scaling 3-state potts and Lee-Yang models” Nuclear Physics B, Volume 342, Issue 3, 8 October 1990, Pages 695-720
Quantum groups
- V. G. Drinfeld, “Quantum groups”, Differential geometry, Lie groups and mechanics. Part VIII, Zap. Nauchn. Sem. LOMI, 155, "Nauka", Leningrad. Otdel., Leningrad, 1986, 18–49; J. Soviet Math., 41:2 (1988), 898–915
- V. G. Drinfeld, “Quantum groups”, Differential geometry, Lie groups and mechanics. Part VIII, Zap. Nauchn. Sem. LOMI, 155, "Nauka", Leningrad. Otdel., Leningrad, 1986, 18–49; J. Soviet Math., 41:2 (1988), 898–915
2d Integrable Models
- Alexander B. Zamolodchikov, Alexei B. Zamolodchikov “Factorized s Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models”, Annals Phys. 120 (1979) 253-291
- A. M. Polyakov and P. B. Wiegmann “Theory of Nonabelian Goldstone Bosons", Phys.Lett.B 131 (1983) 121-126
- A. M. Polyakov and P. B. Wiegmann, “Goldstone Fields in Two-Dimensions with Multivalued Actions” Phys. Lett. 141B, 223 (1984).
- Alexander B. Zamolodchikov, Alexei B. Zamolodchikov “Factorized s Matrices in Two-Dimensions as the Exact Solutions of Certain Relativistic Quantum Field Models”, Annals Phys. 120 (1979) 253-291
- A. M. Polyakov and P. B. Wiegmann “Theory of Nonabelian Goldstone Bosons", Phys.Lett.B 131 (1983) 121-126
- A. M. Polyakov and P. B. Wiegmann, “Goldstone Fields in Two-Dimensions with Multivalued Actions” Phys. Lett. 141B, 223 (1984).
Lattice models
- R. J. Baxter, “Exactly solved models in statistical mechanics,” Courier Corporation, 2007
- R. J. Baxter, “Exactly solved models in statistical mechanics,” Courier Corporation, 2007
Integrability in AdS/CFT
- N. Beisert et al., “Review of AdS/CFT Integrability: An Overview,” Lett. Math. Phys. 99, 3 (2012) doi:10.1007/s11005-011-0529-2 [arXiv:1012.3982 [hep-th]].
- Patrick Dorey, Gregory Korchemsky, Nikita Nekrasov, Volker Schomerus, Didina Serban, and Leticia Cugliandolo “Integrability: From Statistical Systems to Gauge Theory: Lecture Notes of the Les Houches Summer School”: Volume 106, June 2016
- N. Beisert et al., “Review of AdS/CFT Integrability: An Overview,” Lett. Math. Phys. 99, 3 (2012) doi:10.1007/s11005-011-0529-2 [arXiv:1012.3982 [hep-th]].
- Patrick Dorey, Gregory Korchemsky, Nikita Nekrasov, Volker Schomerus, Didina Serban, and Leticia Cugliandolo “Integrability: From Statistical Systems to Gauge Theory: Lecture Notes of the Les Houches Summer School”: Volume 106, June 2016
Integrable field theory and CFT
- V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, “Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz” Commun. Math. Phys. 177 (1996), 381-398; arXiv:hep-th/9412229.
- V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, “Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation” Commun. Math. Phys. 190 (1997), 247-278; arXiv:hep-th/9604044.
- V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, “Integrable Structure of Conformal Field Theory III. The Yang-Baxter relation” Commun. Math. Phys. 200 (1999), 297-324 ; arXiv:hep-th/9805008.
- V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, “Integrable quantum field theories in finite volume: Excited state energies “ Nucl. Phys. B 489 (1997), 487-531; arXiv:hep-th/9607099.
- Patrick Dorey, Roberto Tateo, "Excited states by analytic continuation of TBA equations", Nucl.Phys.B 482 (1996) 639-659 ; arXiv:hep-th/9607167.
- V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, “Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz” Commun. Math. Phys. 177 (1996), 381-398; arXiv:hep-th/9412229.
- V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, “Integrable Structure of Conformal Field Theory II. Q-operator and DDV equation” Commun. Math. Phys. 190 (1997), 247-278; arXiv:hep-th/9604044.
- V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, “Integrable Structure of Conformal Field Theory III. The Yang-Baxter relation” Commun. Math. Phys. 200 (1999), 297-324 ; arXiv:hep-th/9805008.
- V.V. Bazhanov, S.L. Lukyanov and A.B. Zamolodchikov, “Integrable quantum field theories in finite volume: Excited state energies “ Nucl. Phys. B 489 (1997), 487-531; arXiv:hep-th/9607099.
- Patrick Dorey, Roberto Tateo, "Excited states by analytic continuation of TBA equations", Nucl.Phys.B 482 (1996) 639-659 ; arXiv:hep-th/9607167.