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References
M. Forger: "Instantons in Nonlinear σ-Models, Gauge Theories and General Relativity." In: Differential Geometric Methods in Mathematical Physics. Proceedings, Clausthal, Germany 1978; editor: H.D. Doebner. In: Lecture Notes in Physics, Vol. 139, Springer-Verlag, Berlin-Heidelberg-New York, 1981.
M. Forger: "Differential Geometric Methods in Nonlinear σ-Models and Gauge Theories." PhD thesis, Freie Universität Berlin, 1980 (unpublished).
D. Maison: "Some Facts about Classical Nonlinear σ-Models." Max-Planck-Institute preprint MPI-PAE/PTh 52/79, to appear in the Proceedings of the 17th Winter School of Theoretical Physics held in Karpacz, Poland, 1980.
J. Eells, J.H. Sampson: Am.J.Math. 86, 109–160 (1964)
J. Eells, L. Lemaire: Bull.London Math.Soc. 10, 1–68 (1978)
A.C. Scott, F.Y.F. Chu, D.W. McLaughlin: Proc.IEEE 61, 1443–1483 (1973)
K. Lonngren, A.C. Scott (editors): "Solitons in Action." Proceedings, Redstone Arsenal, USA, 1977. Academic Press, New York, 1978.
R.K. Bullough, P.J. Caudrey (editors): "Solitons." In: Topics in Current Physics, Vol. 17, Springer-Verlag, Berlin-Heidelberg-New York, 1980.
M.J. Ablowitz, D.J. Kaup, A.C. Newell, H. Segur: Phys.Rev.Letters 31, 125–127 (1973); Stud.Appl.Math. 53, 249–315 (1974)
C.S. Gardner, J.H. Greene, M.D. Kruskal, R.M. Miura: Phys.Rev.Letters 19, 1095–1097 (1967); Comm.Pure Appl.Math. 27, 97–133 (1974)
V.E. Zakharov, A.B. Shabat: Sov.Phys. JETP 34, 62–69 (1972)
M.J. Ablowitz, D.J. Kaup, A.C. Newell, H. Segur: Phys.Rev.Letters 30, 1262–1264 (1973)
L.A. Takhtajan, L.D. Faddeev: Theor.Math.Phys. 21, 1046–1057 (1974)
F. Lund: Ann.Phys. 115 251–268 (1978)
L.A. Takhtajan: Phys.Lett. 64A, 235–237 (1977)
J. Dieudonné: "Foundations of Modern Analysis." Academic Press, New York, 1969
P. Lax: Comm.Pure Appl.Math. 21, 467 (1968)
L. Faddeev: "Quantum Scattering Transformation." In: Structural Elements in Particle Physics and Statistical Mechanics. Proceedings, Freiburg, Germany 1981; editors: J. Honerkamp, K. Pohlmeyer, H. Römer. In: NATO Advanced Study Institute Series, Vol. B 82, Plenum Press, New York, 1983.
P.P. Kulish, E.K. Sklyanin: "Quantum Spectral Transform Method. Recent Developments." In: Integrable Quantum Field Theories. Proceedings, Tvärminne, Finland, 1981; editors: J. Hietarinta, C. Montonen. In: Lecture Notes in Physics, Vol. 151, Springer-Verlag, Berlin-Heidelberg-New York, 1982.
K. Pohlmeyer: Commun.Math.Phys. 46, 207–221 (1976)
M. Lüscher, K. Pohlmeyer: Nucl.Phys. B 137, 46–54 (1978)
H. Eichenherr, M. Forger: Nucl.Phys. B 155, 381–393 (1979)
H. Eichenherr, M. Forger: Nucl.Phys. B 164, 528–535 (1980)
H. Eichenherr, M. Forger: Commun.Math.Phys. 82, 227–255 (1981)
H. Eichenherr: "Generalized Non-Linear Sigma Models." In: Current Topics in Elementary Particle Physics. Proceedings, Bad Honnef, Germany 1980; editors: K.H. Mütter, K. Schilling. In: NATO Advanced Study Institute Series, Vol. B 70, Plenum Press, New York, 1981.
H. Eichenherr: "Geometric Analysis of Integrable Non-Linear Sigma Models." In: Integrable Quantum Field Theories. Proceedings, Tvärminne, Finland 1981; editors: J. Hietarinta, C. Montonen. In: Lecture Notes in Physics, Vol. 151, Springer-Verlag, Berlin-Heidelberg-New York, 1982.
M. Gell-Mann, M. Lévy: Nuov.Cim. 16, 705–726 (1960)
B.W. Lee: "Chiral Dynamics." Gordon and Breach, New York, 1972.
C. Itzykson, J.B. Zuber: "Quantum Field Theory." McGraw-Hill, New York, 1980.
V.E. Zakharov, A.V. Mikhailov: Sov.Phys. JETP 47, 1017–1027 (1978)
K. Pohlmeyer, K.H. Rehren: J.Math.Phys. 20, 2628–2632 (1979)
A.T. Ogielski, M.K. Prasad, A. Sinha, L.L. Chau-Wang: Phys.Lett. 91 B, 387–391 (1980)
H. Eichenherr: Nucl.Phys. B 146, 215–223 (1978); B 155, 544 (1979)
H. Eichenherr, J. Honerkamp: J.Math.Phys. 22, 374–376 (1981)
H. Eichenherr: Phys.Lett. 90 B, 121–124 (1980)
R. D'Auria, T. Regge, S. Sciuto: Nucl.Phys. B 171, 167–188 (1980)
M. Caselle, R. Megna, S. Sciuto: Nuov.Cim. 63A, 339–352 (1981)
I.V. Cherednik: Theor.Math.Phys. 38, 120–124 (1979); 41, 997–1002 (1979)
K. Scheler: Z.Phys.C-Particles and Fields 6, 365–369 (1980)
K.C. Chou, X.C. Song: "Bäcklund Transformations, Local and Nonlocal Conservation Laws for Nonlinear σ-Models on Symmetric Coset Spaces" and "Local Conservation Laws for Various Nonlinear σ-Models". Academica Sinica preprints ASITP 80–008 and 80–010 (1980)
R. Flume, S. Meyer: Phys.Lett. 85 B, 353–356 (1979)
S. Kobayashi, K. Nomizu: "Foundations of Differential Geometry." Interscience, New York, 1963 (Vol.1) and 1969 (Vol.2).
L.D. Faddeev, M.A. Semenov-Tjan'Shansky: Leningrad University Vestnik 13, 81–88 (1977) (in Russian)
E. Cartan: Bull.Soc.Math.France 54, 214–264 (1926); 55, 114–134 (1927)
S. Helgason: "Differential Geometry, Lie Groups, and Symmetric Spaces." Academic Press, New York, 1978.
S.B. Myers, N. Steenrod: Ann.Math. 40, 400–416 (1939)
W.H. Greub: "Linear Algebra." Springer-Verlag, Berlin-Heidelberg-New York, 1967.
D. Ferus: Math.Ann. 247, 81–93 (1980)
M. Lüscher: Nucl.Phys. B 135, 1–19 (1978)
E. Abdalla, M.C.B. Abdalla, M. Gomes: Phys.Rev. D 23, 1800–1805 (1981)
E. Abdalla, M. Forger, M. Gomes: Nucl.Phys. B 210 [FS 6], 181–192 (1982)
A.M. Polyakov: Phys.Lett. 72 B, 224–226 (1977)
I.Ya.Aref'eva, P.P.Kulish, E.R. Nissimov, S.J. Pacheva: "Infinite Set of Conservation Laws of the Quantum Chiral Field in two-dimensional Space-Time". Leningrad preprint LOMI E-1-1978 (1978)
J.H. Lowenstein, E.R. Speer: Nucl.Phys. B 158, 397–409 (1979)
R. Heidenreich, H. Kluberg-Stern: Nucl.Phys. B 182, 205–241 (1981)
R. Heidenreich: "The Polyakov Currents in the Perturbative Phase of the Nonlinear O(N) Sigma Model." PhD thesis, Freie Universität Berlin, 1980 (unpublished)
Y.Y. Goldschmidt, E. Witten: Phys.Lett. 91 B, 392–396 (1980)
A.B. Zamolodchikov, Al.B. Zamolodchikov: Nucl.Phys. B 133, 525–535 (1978)
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Forger, M. (1983). Nonlinear sigma models on symmetric spaces. In: Andersson, S.I., Doebner, HD. (eds) Non-linear Partial Differential Operators and Quantization Procedures. Lecture Notes in Mathematics, vol 1037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073169
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