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TMF, 1979, Volume 40, Number 2, Pages 194–220 (Mi tmf2888)  

This article is cited in 134 scientific papers (total in 136 papers)

Quantum inverse problem method. I

E. K. Sklyanin, L. A. Takhtadzhyan, L. D. Faddeev

Abstract: A quantum-mechanical variant of the inverse problem method is proposed. For the quantum sine-Gordon model, an exact solution and quantum analogs of action-angle variables are obtained. The connection between the proposed method and Bethe's formulation is discussed, and also renormalization problems.

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Theoretical and Mathematical Physics, 1979, 40:2, 688–706

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Received: 17.04.1979

Citation: E. K. Sklyanin, L. A. Takhtadzhyan, L. D. Faddeev, “Quantum inverse problem method. I”, TMF, 40:2 (1979), 194–220; Theoret. and Math. Phys., 40:2 (1979), 688–706

Citation in format AMSBIB
\by E.~K.~Sklyanin, L.~A.~Takhtadzhyan, L.~D.~Faddeev
\paper Quantum inverse problem method.~I
\jour TMF
\yr 1979
\vol 40
\issue 2
\pages 194--220
\jour Theoret. and Math. Phys.
\yr 1979
\vol 40
\issue 2
\pages 688--706

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    This publication is cited in the following articles:
    1. L. A. Takhtadzhyan, L. D. Faddeev, “The quantum method of the inverse problem and the Heisenberg $XYZ$ model”, Russian Math. Surveys, 34:5 (1979), 11–68  mathnet  crossref  mathscinet
    2. S. A. Tsyplyaev, “Commutation relations of the transition matrix in the classical and quantum inverse scattering methods (local case)”, Theoret. and Math. Phys., 48:1 (1981), 580–586  mathnet  crossref  mathscinet  isi
    3. S. A. Bulgadaev, “Phase transitions in gases with generalized charges interacting through a logarithmic law I. $d=2$, Isotropic case”, Theoret. and Math. Phys., 49:1 (1981), 897–907  mathnet  crossref  mathscinet  isi
    4. N. M. Bogolyubov, “On the physical sector of the lattice sine-Gordon model”, Theoret. and Math. Phys., 51:3 (1982), 540–547  mathnet  crossref  mathscinet  isi
    5. V. V. Bazhanov, Yu. G. Stroganov, “Conditions of commutativity of transfer matrices on a multidimensional lattice”, Theoret. and Math. Phys., 52:1 (1982), 685–691  mathnet  crossref  mathscinet  isi
    6. F. A. Smirnov, “Connection between the sine-Gordon model and the massive bose thirring model”, Theoret. and Math. Phys., 53:3 (1982), 1153–1160  mathnet  crossref  mathscinet  isi
    7. K. A. Sveshnikov, “Covariant perturbation theory in the neighborhood of a classical solution”, Theoret. and Math. Phys., 55:3 (1983), 553–568  mathnet  crossref  mathscinet  isi
    8. A. A. Zheltukhin, “Gauge description and nonlinear string equations in $d$-dimensional space-time”, Theoret. and Math. Phys., 56:2 (1983), 785–795  mathnet  crossref  mathscinet  zmath  isi
    9. V. I. Vichirko, N. Yu. Reshetikhin, “Excitation spectrum of the anisotropic generalization of an $SU_3$ magnet”, Theoret. and Math. Phys., 56:2 (1983), 805–812  mathnet  crossref  mathscinet  isi
    10. V. O. Tarasov, L. A. Takhtadzhyan, L. D. Faddeev, “Local Hamiltonians for integrable quantum models on a lattice”, Theoret. and Math. Phys., 57:2 (1983), 1059–1073  mathnet  crossref  mathscinet  isi
    11. N. M. Bogolyubov, A. G. Izergin, “Lattice completely integrable regularization of the sine-Gordon model for small coupling constants”, Theoret. and Math. Phys., 59:2 (1984), 441–452  mathnet  crossref  mathscinet  isi
    12. F. A. Smirnov, “Quantum Gel'fand–Levitan–Marchenko equations for the sine-Gordon model”, Theoret. and Math. Phys., 60:3 (1984), 871–880  mathnet  crossref  mathscinet  isi
    13. V. O. Tarasov, “Structure of quantum L operators for the R matrix of the XXZ model”, Theoret. and Math. Phys., 61:2 (1984), 1065–1072  mathnet  crossref  mathscinet  isi
    14. N. M. Bogolyubov, A. G. Izergin, “Lattice sine-Gordon model with local Hamiltonian”, Theoret. and Math. Phys., 61:3 (1984), 1195–1204  mathnet  crossref  mathscinet  isi
    15. I. M. Khamitov, “Local fields in the inverse scattering method”, Theoret. and Math. Phys., 62:3 (1985), 217–224  mathnet  crossref  mathscinet  isi
    16. F. A. Smirnov, “Solution of quantum Gel'fand–Levitan–Marchenko equations for the sine-gordon model in the soliton sector for $\gamma=\pi/\nu$”, Theoret. and Math. Phys., 67:1 (1986), 344–351  mathnet  crossref  mathscinet  isi
    17. V. O. Tarasov, “Algebraic bethe ansatz for the Izergin–Korepin $R$ matrix”, Theoret. and Math. Phys., 76:2 (1988), 793–803  mathnet  crossref  mathscinet  isi
    18. M. V. Karasev, V. P. Maslov, “Non-Lie permutation relations”, Russian Math. Surveys, 45:5 (1990), 51–98  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    19. D. V. Yur'ev, “Quantum conformal field theory as an infinite-dimensional non-commutative geometry”, Russian Math. Surveys, 46:4 (1991), 135–163  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    20. A. Yu. Volkov, L. D. Faddeev, “Quantum inverse scattering method on a spacetime lattice”, Theoret. and Math. Phys., 92:2 (1992), 837–842  mathnet  crossref  mathscinet  isi
    21. S. A. Bychkov, D. V. Yur'ev, “Three algebraic structures of quantum projective ($\mathrm{sl}(2,\mathbb C)$-invariant) field theory”, Theoret. and Math. Phys., 97:3 (1993), 1333–1339  mathnet  crossref  mathscinet  zmath  isi
    22. Yu. S. Osipov, A. A. Gonchar, S. P. Novikov, V. I. Arnol'd, G. I. Marchuk, P. P. Kulish, V. S. Vladimirov, E. F. Mishchenko, “Lyudvig Dmitrievich Faddeev (on his sixtieth birthday)”, Russian Math. Surveys, 50:3 (1995), 643–659  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    23. K. A. Sveshnikov, P. K. Silaev, “Connection between discontinuous step-like and smooth kink-type classical solutions in quantum field theory”, Theoret. and Math. Phys., 108:2 (1996), 1019–1045  mathnet  crossref  crossref  mathscinet  zmath  isi
    24. A. V. Antonov, “Quantum Volterra model and universal $R$-matrix”, Theoret. and Math. Phys., 113:3 (1997), 1520–1529  mathnet  crossref  crossref  mathscinet  zmath  isi
    25. Karowski, M, “A lattice model of local algebras of observables and fields with braid group statistics”, Helvetica Physica Acta, 70:1–2 (1997), 192  isi
    26. N. M. Bogolyubov, A. G. Izergin, A. L. Kitanin, A. G. Pronko, “The Probabilities of Survival and Hopping of States in the Phase Model on a Finite Lattice”, Proc. Steklov Inst. Math., 226 (1999), 29–41  mathnet  mathscinet  zmath
    27. V. E. Korepin, N. A. Slavnov, “The Form Factors in a Finite Volume”, Proc. Steklov Inst. Math., 226 (1999), 72–85  mathnet  mathscinet  zmath
    28. D'Hoker E., Phong D.H., “Lectures on supersymmetric Yang-Mills theory and integrable systems”, Theoretical Physics At the End of the Twentieth Century, CRM Series in Mathematical Physics, 2002, 1–125  isi
    29. D. R. Karakhanyan, “Representations of the Quantum Group $SL_q(2)$ in a Space of Functions”, Theoret. and Math. Phys., 134:3 (2003), 326–332  mathnet  crossref  crossref  mathscinet  zmath  isi
    30. D. R. Karakhanyan, “Realization of the Universal $s\ell_q(2)$-Symmetric $R$-Operator in a Function Space for General and Exceptional Values of the Deformation Parameter”, Theoret. and Math. Phys., 135:2 (2003), 614–637  mathnet  crossref  crossref  mathscinet  zmath  isi
    31. N. A. Slavnov, “Integral Representations for Correlation Functions of the $XXZ$ Heisenberg Chain”, Theoret. and Math. Phys., 135:3 (2003), 828–835  mathnet  crossref  crossref  mathscinet  zmath  isi
    32. Korff, C, “Auxiliary matrices for the six-vertex model at q(N)=1 and a geometric interpretation of its symmetries”, Journal of Physics A-Mathematical and General, 36:19 (2003), 5229  crossref  isi
    33. N. A. Slavnov, “On Scalar Products in the Algebraic Bethe Ansatz”, Proc. Steklov Inst. Math., 251 (2005), 246–253  mathnet  mathscinet  zmath
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    35. Mesref, L, “Quantum field theories”, International Journal of Modern Physics A, 20:23 (2005), 5317  crossref  isi
    36. Doikou, A, “From affine Hecke algebras to boundary symmetries”, Nuclear Physics B, 725:3 (2005), 493  crossref  isi
    37. Korff C., “Solving Baxter's TQ-equation via representation theory”, Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemporary Mathematics Series, 391, 2005, 199–211  crossref  isi
    38. I. E. Shenderovich, “Local Hamiltonian in the Faddeev–Tirkkonen model”, J. Math. Sci. (N. Y.), 143:1 (2007), 2840–2844  mathnet  crossref  mathscinet  zmath
    39. Sergey É Derkachov, Alexander N. Manashov, “$\mathcal R$-Matrix and Baxter $\mathcal Q$-Operators for the Noncompact $\mathrm{SL}(N,\mathbb C)$ Invariant Spin Chain”, SIGMA, 2 (2006), 084, 20 pp.  mathnet  crossref  mathscinet  zmath
    40. Kundu, A, “Unifying quantization for inhomogeneous integrable models”, Physics Letters B, 633:4–5 (2006), 657  crossref  isi
    41. N. A. Slavnov, “The algebraic Bethe ansatz and quantum integrable systems”, Russian Math. Surveys, 62:4 (2007), 727–766  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    42. A. Kundu, “Yang–Baxter algebra and generation of quantum integrable models”, Theoret. and Math. Phys., 151:3 (2007), 831–842  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    43. P. P. Kulish, N. Manoilovich, “Quantum algebras with representation ring of $\operatorname{sl}(2)$ type”, J. Math. Sci. (N. Y.), 151:2 (2008), 2894–2900  mathnet  crossref  mathscinet  elib
    44. Bazhanov, VV, “Analytic theory of the eight-vertex model”, Nuclear Physics B, 775:3 (2007), 225  crossref  isi
    45. Caux, JS, “One-particle dynamical correlations in the one-dimensional Bose gas”, Journal of Statistical Mechanics-Theory and Experiment, 2007, P01008  isi
    46. V. P. Spiridonov, “Essays on the theory of elliptic hypergeometric functions”, Russian Math. Surveys, 63:3 (2008), 405–472  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    47. Bazhanov, VV, “Baxter's Q-operators for supersymmetric spin chains”, Nuclear Physics B, 805:3 (2008), 451  crossref  mathscinet  adsnasa  isi
    48. Belliard, S, “The nested Bethe ansatz for 'all' closed spin chains”, Journal of Physics A-Mathematical and Theoretical, 41:29 (2008), 295202  crossref  mathscinet  zmath  isi
    49. Kundu, A, “Changing Solitons in Classical & Quantum Integrable Defect and Variable Mass sine-Gordon Model”, Journal of Nonlinear Mathematical Physics, 15 (2008), 237  crossref  isi
    50. Habibullin, I, “Quantum and classical integrable sine-Gordon model with defect”, Nuclear Physics B, 795:3 (2008), 549  crossref  isi
    51. Belliard, S, “The nested Bethe ansatz for 'all' open spin chains with diagonal boundary conditions”, Journal of Physics A-Mathematical and Theoretical, 42:20 (2009), 205203  crossref  zmath  adsnasa  isi
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    56. St. Petersburg Math. J., 22:3 (2011), 437–446  mathnet  crossref  mathscinet  zmath  isi
    57. Samuel Belliard, Stanislav Pakuliak, Eric Ragoucy, “Universal Bethe Ansatz and Scalar Products of Bethe Vectors”, SIGMA, 6 (2010), 094, 22 pp.  mathnet  crossref  mathscinet
    58. Ghali Filali, Nikolai Kitanine, “Spin Chains with Non-Diagonal Boundaries and Trigonometric SOS Model with Reflecting End”, SIGMA, 7 (2011), 012, 22 pp.  mathnet  crossref  mathscinet
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    60. Santos G., “Exactly solvable models for multiatomic molecular Bose–Einstein condensates”, J. Phys. A: Math. Theor., 44:34 (2011), 345003  crossref  isi
    61. Baseilhac P., Belliard S., “The central extension of the reflection equations and an analog of Miki's formula”, J. Phys. A: Math. Theor., 44:41 (2011), 415205  crossref  isi
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    63. Nekrasov N., Rosly A., Shatashvili S., “Darboux coordinates, Yang-Yang functional, and gauge theory”, Nuclear Phys B Proc Suppl, 216 (2011), 69–93  crossref  isi
    64. Kozlowski K.K., Terras V., “Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schrodinger model”, J Stat Mech Theory Exp, 2011, P09013  isi
    65. Kozlowski K.K., Maillet J.M., Slavnov N.A., “Long-distance behavior of temperature correlation functions in the one-dimensional Bose gas”, J Stat Mech Theory Exp, 2011, P03018  isi
    66. Ridout D., Teschner J., “Integrability of a family of quantum field theories related to sigma models”, Nuclear Phys B, 853:2 (2011), 327–378  crossref  isi
    67. Galleas W., “Multiple integral representation for the trigonometric SOS model with domain wall boundaries”, Nuclear Phys B, 858:1 (2012), 117–141  crossref  isi
    68. Rubeni D., Foerster A., Mattei E., Roditi I., “Quantum phase transitions in Bose–Einstein condensates from a Bethe ansatz perspective”, Nuclear Phys B, 856:3 (2012), 698–715  crossref  isi
    69. Chicherin D., Derkachov S., Karakhanyan D., Kirschner R., “Baxter operators for arbitrary spin II”, Nuclear Phys B, 854:2 (2012), 433–465  crossref  isi
    70. N. M. Bogoliubov, P. P. Kulish, “Exactly solvable models of quantum nonlinear optics”, J. Math. Sci. (N. Y.), 192:1 (2013), 14–30  mathnet  crossref  mathscinet
    71. Grosjean N. Niccoli G., “The Tau(2)-Model and the Chiral Potts Model Revisited: Completeness of Bethe Equations From Sklyanin's Sov Method”, J. Stat. Mech.-Theory Exp., 2012, P11005  crossref  isi
    72. N. A. Slavnov, “Asymptotic expansions for correlation functions of one-dimensional bosons”, Theoret. and Math. Phys., 174:1 (2013), 109–121  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    73. Levin A. Olshanetsky M. Smirnov A. Zotov A., “Characteristic Classes of Sl(N, C)-Bundles and Quantum Dynamical Elliptic R-Matrices”, J. Phys. A-Math. Theor., 46:3 (2013), 035201  crossref  isi
    74. Finch P.E., “From Spin to Anyon Notation: the Xxz Heisenberg Model as a D-3 (Or Su(2)(4)) Anyon Chain”, J. Phys. A-Math. Theor., 46:5 (2013), 055305  crossref  isi
    75. L. D. Faddeev, “The new life of complete integrability”, Phys. Usp., 56:5 (2013), 465–472  mathnet  crossref  crossref  adsnasa  isi  elib  elib
    76. JETP Letters, 97:1 (2013), 45–51  mathnet  crossref  crossref  isi  elib  elib
    77. Samuel Belliard, Stanislav Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Bethe Vectors of Quantum Integrable Models with $\mathrm{GL}(3)$ Trigonometric $R$-Matrix”, SIGMA, 9 (2013), 058, 23 pp.  mathnet  crossref  mathscinet
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    79. Samuel Belliard, Nicolas Crampé, “Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz”, SIGMA, 9 (2013), 072, 12 pp.  mathnet  crossref  mathscinet
    80. Santos G., Foerster A., Roditi I., “A Bosonic Multi-State Two-Well Model”, J. Phys. A-Math. Theor., 46:26 (2013)  crossref  isi
    81. Motegi K., “On Baxter's Q Operator of the Higher Spin Xxz Chain at the Razumov-Stroganov Point”, J. Math. Phys., 54:6 (2013), 063510  crossref  isi
    82. Belliard S., Pakuliak S., Ragoucy E., Slavnov N.A., “Bethe Vectors of Gl(3)-Invariant Integrable Models”, J. Stat. Mech.-Theory Exp., 2013, P02020  crossref  isi
    83. Galleas W., “Functional Relations and the Yang–Baxter Algebra”, Xxist International Conference on Integrable Systems and Quantum Symmetries (Isqs21), Journal of Physics Conference Series, 474, ed. Burdik C. Navratil O. Posta S., IOP Publishing Ltd, 2013  crossref  isi
    84. Antonio N.C. Manojlovic N. Nagy Z., “Trigonometric Sl (2) Gaudin Model with Boundary Terms”, Rev. Math. Phys., 25:10, SI (2013), 1343004  crossref  isi
    85. S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Scalar products in models with a $GL(3)$ trigonometric $R$-matrix: Highest coefficient”, Theoret. and Math. Phys., 178:3 (2014), 314–335  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    86. Gorsky A., Zabrodin A., Zotov A., “Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems”, J. High Energy Phys., 2014, no. 1, 070, 1–28  crossref  isi
    87. S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Scalar products in models with the $GL(3)$ trigonometric $R$-matrix: General case”, Theoret. and Math. Phys., 180:1 (2014), 795–814  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
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    92. Mangazeev V.V., “Q-Operators in the Six-Vertex Model”, Nucl. Phys. B, 886 (2014), 166–184  crossref  isi
    93. Derkachov S.E., Manashov A.N., “Iterative Construction of Eigenfunctions of the Monodromy Matrix For Sl(2, C) Magnet”, J. Phys. A-Math. Theor., 47:30 (2014), 305204  crossref  isi
    94. Levin A. Olshanetsky M. Zotov A., “Relativistic Classical Integrable Tops and Quantum R-Matrices”, J. High Energy Phys., 2014, no. 7, 012  crossref  isi
    95. Mangazeev V.V., “On the Yang–Baxter Equation For the Six-Vertex Model”, Nucl. Phys. B, 882 (2014), 70–96  crossref  isi
    96. Kiselev A.V., Krutov A.O., “Non-Abelian Lie Algebroids Over Jet Spaces”, J. Nonlinear Math. Phys., 21:2 (2014), 188–213  crossref  isi
    97. Kozlowski K.K., “Unitarity of the Sov Transform For the Toda Chain”, Commun. Math. Phys., 334:1 (2015), 223–273  crossref  isi
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    102. Samuel Belliard, Rodrigo A. Pimenta, “Slavnov and Gaudin–Korepin Formulas for Models without $\mathrm{U}(1)$ Symmetry: the Twisted XXX Chain”, SIGMA, 11 (2015), 099, 12 pp.  mathnet  crossref
    103. Arthur Hutsalyuk, Andrii Liashyk, Stanislav Z. Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Multiple actions of the monodromy matrix in $\mathfrak{gl}(2|1)$-invariant integrable models”, SIGMA, 12 (2016), 099, 22 pp.  mathnet  crossref  mathscinet  elib
    104. N. A. Slavnov, “Multiple commutation relations in the models with $\mathfrak gl(2|1)$ symmetry”, Theoret. and Math. Phys., 189:2 (2016), 1624–1644  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    105. B. L. Feigin, “Integrable systems, shuffle algebras, and Bethe equations”, Trans. Moscow Math. Soc., 77 (2016), 203–246  mathnet  crossref  elib
    106. Hutsalyuk A. Liashyk A. Pakuliak S.Z. Ragoucy E. Slavnov N.A., “Scalar products of Bethe vectors in models with ${\mathfrak{gl}}(2| 1)$ symmetry 1. Super-analog of Reshetikhin formula”, J. Phys. A-Math. Theor., 49:45 (2016), 454005, 1–28  crossref  mathscinet  isi  scopus
    107. Sechin I., Zotov A., “Associative Yang–Baxter equation for quantum (semi-)dynamical R-matrices”, J. Math. Phys., 57:5 (2016), 053505  crossref  mathscinet  zmath  isi  elib  scopus
    108. Kozlowski K.K., Ragoucy E., “Asymptotic behaviour of two-point functions in multi-species models”, Nucl. Phys. B, 906 (2016), 241–288  crossref  mathscinet  zmath  isi  elib  scopus
    109. A. A. Hutsalyuk, A. Liashyk, S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Current presentation for the super-Yangian double $DY(\mathfrak{gl}(m|n))$ and Bethe vectors”, Russian Math. Surveys, 72:1 (2017), 33–99  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    110. Samuel Belliard, Vidas Regelskis, “Drinfeld J Presentation of Twisted Yangians”, SIGMA, 13 (2017), 011, 35 pp.  mathnet  crossref
    111. Jan Fuksa, “Bethe Vectors for Composite Models with $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(1|2)$ Supersymmetry”, SIGMA, 13 (2017), 015, 17 pp.  mathnet  crossref
    112. Dorey N., Zhao P., “Solution of quantum integrable systems from quiver gauge theories”, J. High Energy Phys., 2017, no. 2, 118  crossref  mathscinet  isi  scopus
    113. N. A. Slavnov, “Algebraicheskii anzats Bete”, Lekts. kursy NOTs, 27, MIAN, M., 2017, 3–189  mathnet  crossref  elib
    114. Qinxiu Sun, Fang Li, “A generalization of Lie $H$-pseudo-bialgebras”, Theoret. and Math. Phys., 192:1 (2017), 939–957  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    115. E. V. Damaskinsky, M. A. Sokolov, “The generating function of bivariate Chebyshev polynomials associated with the Lie algebra $G_2$”, Theoret. and Math. Phys., 192:2 (2017), 1115–1128  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    116. D. R. Karakhanyan, R. Kirshner, “Second-order evaluations of orthogonal and symplectic Yangians”, Theoret. and Math. Phys., 192:2 (2017), 1154–1161  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    117. L. A. Takhtajan, A. Yu. Alekseev, I. Ya. Aref'eva, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, S. L. Shatashvili, “Scientific heritage of L. D. Faddeev. Survey of papers”, Russian Math. Surveys, 72:6 (2017), 977–1081  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    118. Hutsalyuk A. Liashyk A. Pakuliak S.Z. Ragoucy E. Slavnov N.A., “Scalar Products of Bethe Vectors in the Models With Gl(M|N) Symmetry”, Nucl. Phys. B, 923 (2017), 277–311  crossref  isi
    119. Derkachov S.E., Manashov A.N., Valinevich P.A., “Gustafson Integrals For Sl(2, C) Spin Magnet”, J. Phys. A-Math. Theor., 50:29 (2017), 294007  crossref  isi
    120. Derkachov S.E., Manashov A.N., “Spin Chains and Gustafson'S Integrals”, J. Phys. A-Math. Theor., 50:29 (2017), 294006  crossref  isi
    121. Fuksa J., Slavnov N.A., “Form Factors of Local Operators in Supersymmetric Quantum Integrable Models”, J. Stat. Mech.-Theory Exp., 2017, 043106  crossref  isi
    122. Hutsalyuk A., Liashyk A., Pakuliak S.Z., Ragoucy E., Slavnov N.A., “Scalar Products of Bethe Vectors in Models With Gl(2 Vertical Bar 1) Symmetry 2. Determinant Representation”, J. Phys. A-Math. Theor., 50:3 (2017), 034004  crossref  isi
    123. P. A. Valinevich, S. E. Derkachev, A. P. Isaev, A. V. Komisarchuk, “Ortogonalnye polinomy, 6j-simvoly i statisticheskie vesa SOS-modelei”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 24, Zap. nauchn. sem. POMI, 465, POMI, SPb., 2017, 105–134  mathnet
    124. James A.J.A. Konik R.M. Lecheminant Ph. Robinson N.J. Tsvelik A.M., “Non-Perturbative Methodologies For Low-Dimensional Strongly-Correlated Systems: From Non-Abelian Bosonization to Truncated Spectrum Methods”, Rep. Prog. Phys., 81:4 (2018), 046002  crossref  isi
    125. Hutsalyuk A. Liashyk A. Pakuliak S.Z. Ragoucy E. Slavnov N.A., “Scalar Products and Norm of Bethe Vectors For Integrable Models Based on U-Q ((Gl)Over-Cap(M))”, SciPost Phys., 4:1 (2018), 006  crossref  isi
    126. Liashyk A. Slavnov N.A., “On Bethe Vectors in Gl(3)-Invariant Integrable Models”, J. High Energy Phys., 2018, no. 6, 018  crossref  isi
    127. Sergey É. Derkachov, Alexander N. Manashov, Pavel A. Valinevich, “$\mathrm{SL}(2,\mathbb{C})$ Gustafson Integrals”, SIGMA, 14 (2018), 030, 16 pp.  mathnet  crossref
    128. Samuel Belliard, Nikita A. Slavnov, Benoit Vallet, “Modified Algebraic Bethe Ansatz: Twisted XXX Case”, SIGMA, 14 (2018), 054, 18 pp.  mathnet  crossref
    129. Belliard S., Slavnov N.A., Vallet B., “Scalar Product of Twisted Xxx Modified Bethe Vectors”, J. Stat. Mech.-Theory Exp., 2018, 093103  crossref  isi  scopus
    130. N. A. Slavnov, “Determinant representations for scalar products in the algebraic Bethe ansatz”, Theoret. and Math. Phys., 197:3 (2018), 1771–1778  mathnet  crossref  crossref  adsnasa  isi  elib
    131. A. V. Zotov, “Calogero–Moser model and $R$-matrix identities”, Theoret. and Math. Phys., 197:3 (2018), 1755–1770  mathnet  crossref  crossref  adsnasa  isi  elib
    132. N. M. Belousov, S. E. Derkachev, “$Q$-operator dlya kvantovoi modeli NSh”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 25, K 70-letiyu M. A. Semenova-Tyan-Shanskogo, Zap. nauchn. sem. POMI, 473, POMI, SPb., 2018, 34–65  mathnet
    133. Gahramanov I. Jafarzade Sh., “Integrable Lattice Spin Models From Supersymmetric Dualities”, Phys. Part. Nuclei Lett., 15:6 (2018), 650–667  crossref  isi  scopus
    134. Litvinov A.V. Spodyneiko L.A., “On Dual Description of the Deformed O(N) SIGMA Model”, J. High Energy Phys., 2018, no. 11, 139  crossref  mathscinet  zmath  isi  scopus
    135. Č. Burdík, O. Navrátil, “Nested Bethe ansatz for the RTT algebra of $sp(4)$ type”, Theoret. and Math. Phys., 198:1 (2019), 1–16  mathnet  crossref  crossref  elib
    136. D. R. Karakhanyan, R. Kirshner, “Orthogonal and symplectic Yangians and Lie algebra representations”, Theoret. and Math. Phys., 198:2 (2019), 239–248  mathnet  crossref  crossref  elib
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