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In these notes we review the S-matrix theory in (1+1)-dimensional integrable models, focusing mainly on the relativistic case.
1924
Earlier work this paper cites.
J. A. Wheeler, “On the mathematical description of light nuclei by the method of resonating group structure”, Phys. Rev. 52
1937
Earlier work this paper cites.
W. Heisenberg, “Der mathematische Rahmen der Quantentheorie der Wellenfelder”, Zeit. für Naturforschung 1
1946
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K. M. Watson, “Some general relations between the photoproduction and scattering of pi mesons”, Phys. Rev. 95
1954
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H. Lehmann, K. Symanzik and W. Zimmermann, “On the formulation of quantized field theories”, Nuovo Cim. 1
1955
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L. Castillejo, R. H. Dalitz and F. J. Dyson, “Low’s scattering equation for the charged and neutral scalar theories”, Phys. Rev. 101
1956
Earlier work this paper cites.
S. Mandelstam, “Determination of the pion - nucleon scattering amplitude from dispersion relations and unitarity. General theory”, Phys. Rev. 112
1958
Earlier work this paper cites.
G. Chew, “The S-matrix theory of strong interaction”, W. A. Benjamin Inc., New York (1961)
1961
Earlier work this paper cites.
S. R. Coleman and J. Mandula, “All possible symmetries of the S-matrix”, Phys. Rev. 159
1967
Earlier work this paper cites.
L. D. Faddeev and L. A. Takhtajan, “Essentially nonlinear one-dimensional model of the classical field theory”, Theor. Math. Phys. 21
1974
Earlier work this paper cites.
I. Arefeva and V. Korepin, “Scattering in two-dimensional model with Lagrangian 1 / γ ( ( d μ u ) 2 / 2 + m 2 cos ( u − 1 ) ) 1/\gamma((d_{\mu}u)^{2}/2+m^{2}\cos(u-1)) ”, Pisma Zh. Eksp. Teor. Fiz. 20
1974
Earlier work this paper cites.
D. J. Gross and A. Neveu, “Dynamical symmetry breaking in asymptotically free field theories”, Phys. Rev. D 10
1974
Earlier work this paper cites.
S. Mandelstam, “Soliton operators for the quantized sine-Gordon equation”, Phys. Rev. D 11
1975
Earlier work this paper cites.
V. E. Korepin and L. D. Faddeev, “Quantization of solitons”, Theor. Math. Phys. 25
1975
Earlier work this paper cites.
V. E. Korepin, P. P. Kulish and L. D. Faddeev, “Soliton quantization”, JETP Lett. 21
1975
Earlier work this paper cites.
R. Jackiw and G. Woo, “Semiclassical scattering of quantized nonlinear waves”, Phys. Rev. D 12
1975
Earlier work this paper cites.
P. P. Kulish and E. R. Nissimov, “Conservation laws in the quantum theory: cos ϕ \cos\phi in two-dimensions and in the massive Thirring model”, JETP Lett. 24
1976
Earlier work this paper cites.
A. M. Polyakov, “Hidden symmetry of the two-dimensional chiral fields”, Phys. Lett. B 72
1977
Earlier work this paper cites.
A. B. Zamolodchikov, “Exact S-matrix of quantum sine-Gordon solitons”, JETP Lett. 25
1977
Earlier work this paper cites.
M. Karowski, H. J. Thun, T. T. Truong and P. H. Weisz, “On the uniqueness of a purely elastic S-matrix in (1+1)-dimensions”, Phys. Lett. B 67
1977
Earlier work this paper cites.
M. Karowski and H. J. Thun, “Complete S-matrix of the massive Thirring model”, Nucl. Phys. B 130
1977
Earlier work this paper cites.
P. H. Weisz, “Exact quantum sine-Gordon soliton form factors”, Phys. Lett. B 67
1977
Earlier work this paper cites.
M. Karowski and P. Weisz, “Exact form factors in (1+1)-dimensional field theoretic models with soliton behavior”, Nucl. Phys. B 139
1978
Earlier work this paper cites.
R. Shankar and E. Witten, “The S-matrix of the supersymmetric nonlinear sigma model”, Phys. Rev. D 17
1978
Earlier work this paper cites.
D. Iagolnitzer, “Factorization of the multiparticle S-matrix in two-dimensional space-time models”, Phys. Rev. D 18
1978
Earlier work this paper cites.
M. Lüscher, “Quantum nonlocal charges and absence of particle production in the two-dimensional nonlinear sigma model”, Nucl. Phys. B 135
1978
Earlier work this paper cites.
A. B. Zamolodchikov and A. B. Zamolodchikov, “Factorized S-matrices in two-dimensions as the exact solutions of certain relativistic quantum field models”, Annals Phys. 120
1979
Earlier work this paper cites.
M. Karowski, “An exact relativistic S-matrix in (1+1)-dimensions: The on-shell solution of the massive Thirring model and the quantum sine-Gordon equation”, Proc. 15th Erice School of Subnuclear Physics: The Why’s of Subnuclear Physics, ed.: A. Zichichi, Plenum Press, New York (1979)
1979
Earlier work this paper cites.
B. Berg, M. Karowski, P. Weisz and V. Kurak, “Factorized U(n) symmetric S-matrices in two-dimensions”, Nucl. Phys. B 134
1979
Earlier work this paper cites.
V. Kurak and J. A. Swieca, “Anti-particles as bound states of particles in the factorized S-matrix framework”, Phys. Lett. B 82
1979
Earlier work this paper cites.
S. J. Parke, “Absence of particle production and factorization of the S-matrix in (1+1)-dimensional models”, Nucl. Phys. B 174
1980
Earlier work this paper cites.
L. D. Faddeev, “Quantum completely integrable models of field theory”, Sov. Sci. Rev. C 1
1980
Cited alongside, same era.
V. G. Drinfeld, “Quantum groups”, J. Sov. Math. 41
1986
Cited alongside, same era.
T. R. Klassen and E. Melzer, “Purely elastic scattering theories and their ultraviolet limits”, Nucl. Phys. B 338
1990
Cited alongside, same era.
M. Lüscher, “On a relation between finite size effects and elastic scattering processes”, in the proceedings of the Cargese Summer Institute: “Progress in gauge field theory”, edited by G. ’t Hooft, A. Singer, R. Stora, Plenum Press, New York (1984); M. Lüscher, “Volume dependence of the energy spectrum in massive quantum field theories. 1. Stable particle states”, Commun. Math. Phys. 104
1991
Cited alongside, same era.
V. P. Yurov and A. B. Zamolodchikov, “Correlation functions of integrable 2-D models of relativistic field theory. Ising model”, Int. J. Mod. Phys. A 6
2009
Later among the works it cites.
N. Gromov and P. Vieira, “The all loop AdS 4
2009
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G. Mussardo, “Statistical field theory, an introduction to exactly solved models in statistical physics”, Oxford University Press, New York (2010)
2010
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2010
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1991
Cited alongside, same era.
F. A. Smirnov,“Form factors in completely integrable models of quantum field theory”, Adv. Series in Math. Phys. 14
1992
Cited alongside, same era.
N. J. MacKay, “On the algebraic structure of factorized S-matrices”, Durham theses, Durham University (1992), http://etheses.dur.ac.uk/5764/
1992
Cited alongside, same era.
T. R. Klassen and E. Melzer, “Sine-Gordon not equal to massive Thirring, and related heresies”, Int. J. Mod. Phys. A 8
1993
Cited alongside, same era.
G. W. Delius, “Exact S-matrices with affine quantum group symmetry”, Nucl. Phys. B 451
1995
Cited alongside, same era.
P. Dorey, “Exact S-matrices”, in the proceedings of the Eötvös Summer School in Physics: “Conformal field theories and integrable models”, edited by Z. Horvath, L. Palla, Springer, Berlin (1997) [hep-th/9810026]
1997
Cited alongside, same era.
H. M. Babujian, A. Fring, M. Karowski and A. Zapletal, “Exact form-factors in integrable quantum field theories: The sine-Gordon model”, Nucl. Phys. B 538
1999
Cited alongside, same era.
J. L. Miramontes, “Hermitian analyticity versus real analyticity in two-dimensional factorized S-matrix theories”, Phys. Lett. B 455
1999
Cited alongside, same era.
2010
Later among the works it cites.
D. Bombardelli, D. Fioravanti and R. Tateo, “TBA and Y-system for planar AdS 4
2010
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2010
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2012
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2012
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2012
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F. Spill, “Yangians in integrable field theories, spin chains and gauge-string dualities”, Rev. Math. Phys. 24
2012
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2012
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C. Ahn and D. Bombardelli, “Exact S-matrices for AdS 3 /CFT 2 ”, Int. J. Mod. Phys. A 28
2013
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2013
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2013
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2013
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2014
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2014
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2014
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G. Delfino, “Fields, particles and universality in two dimensions”, Annals Phys. 360
2015
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N. Beisert, M. de Leeuw and P. Nag, “Fusion for the one-dimensional Hubbard model”, J. Phys. A 48
2015
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2015
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2015
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2015
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2016
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2016
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2016
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2016
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2016
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2016
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S. R. Coleman, “The quantum sine-Gordon equation as the massive Thirring model”, Phys. Rev. D 11
2088
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