Advertisement

Nonlinear sigma models on symmetric spaces

  • Michael Forger
Part I Non-linear Partial Differential Operators
Part of the Lecture Notes in Mathematics book series (LNM, volume 1037)

Keywords

Symmetric Space Integrability Property Weyl Chamber Riemannian Symmetric Space Compact Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1).
    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.CrossRefGoogle Scholar
  2. 2).
    M. Forger: "Differential Geometric Methods in Nonlinear σ-Models and Gauge Theories." PhD thesis, Freie Universität Berlin, 1980 (unpublished).Google Scholar
  3. 3).
    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.Google Scholar
  4. 4).
    J. Eells, J.H. Sampson: Am.J.Math. 86, 109–160 (1964)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 4a).
    J. Eells, L. Lemaire: Bull.London Math.Soc. 10, 1–68 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 5).
    A.C. Scott, F.Y.F. Chu, D.W. McLaughlin: Proc.IEEE 61, 1443–1483 (1973)MathSciNetCrossRefGoogle Scholar
  7. 6).
    K. Lonngren, A.C. Scott (editors): "Solitons in Action." Proceedings, Redstone Arsenal, USA, 1977. Academic Press, New York, 1978.zbMATHGoogle Scholar
  8. 6a).
    R.K. Bullough, P.J. Caudrey (editors): "Solitons." In: Topics in Current Physics, Vol. 17, Springer-Verlag, Berlin-Heidelberg-New York, 1980.Google Scholar
  9. 7).
    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)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 8).
    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)zbMATHCrossRefGoogle Scholar
  11. 9).
    V.E. Zakharov, A.B. Shabat: Sov.Phys. JETP 34, 62–69 (1972)MathSciNetGoogle Scholar
  12. 10).
    M.J. Ablowitz, D.J. Kaup, A.C. Newell, H. Segur: Phys.Rev.Letters 30, 1262–1264 (1973)MathSciNetCrossRefGoogle Scholar
  13. 10a).
    L.A. Takhtajan, L.D. Faddeev: Theor.Math.Phys. 21, 1046–1057 (1974)CrossRefGoogle Scholar
  14. 11).
    F. Lund: Ann.Phys. 115 251–268 (1978)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 12).
    L.A. Takhtajan: Phys.Lett. 64A, 235–237 (1977)MathSciNetGoogle Scholar
  16. 13).
    J. Dieudonné: "Foundations of Modern Analysis." Academic Press, New York, 1969zbMATHGoogle Scholar
  17. 14).
    P. Lax: Comm.Pure Appl.Math. 21, 467 (1968)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 15).
    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.Google Scholar
  19. 15a).
    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.CrossRefGoogle Scholar
  20. 16).
    K. Pohlmeyer: Commun.Math.Phys. 46, 207–221 (1976)MathSciNetzbMATHCrossRefGoogle Scholar
  21. 17).
    M. Lüscher, K. Pohlmeyer: Nucl.Phys. B 137, 46–54 (1978)CrossRefGoogle Scholar
  22. 18).
    H. Eichenherr, M. Forger: Nucl.Phys. B 155, 381–393 (1979)MathSciNetCrossRefGoogle Scholar
  23. 19).
    H. Eichenherr, M. Forger: Nucl.Phys. B 164, 528–535 (1980)MathSciNetCrossRefGoogle Scholar
  24. 20).
    H. Eichenherr, M. Forger: Commun.Math.Phys. 82, 227–255 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 21).
    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.Google Scholar
  26. 22).
    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.CrossRefGoogle Scholar
  27. 23).
    M. Gell-Mann, M. Lévy: Nuov.Cim. 16, 705–726 (1960)zbMATHCrossRefGoogle Scholar
  28. 24).
    B.W. Lee: "Chiral Dynamics." Gordon and Breach, New York, 1972.Google Scholar
  29. 25).
    C. Itzykson, J.B. Zuber: "Quantum Field Theory." McGraw-Hill, New York, 1980.Google Scholar
  30. 26).
    V.E. Zakharov, A.V. Mikhailov: Sov.Phys. JETP 47, 1017–1027 (1978)Google Scholar
  31. 27).
    K. Pohlmeyer, K.H. Rehren: J.Math.Phys. 20, 2628–2632 (1979)MathSciNetCrossRefGoogle Scholar
  32. 28).
    A.T. Ogielski, M.K. Prasad, A. Sinha, L.L. Chau-Wang: Phys.Lett. 91 B, 387–391 (1980)Google Scholar
  33. 29).
    H. Eichenherr: Nucl.Phys. B 146, 215–223 (1978); B 155, 544 (1979)CrossRefGoogle Scholar
  34. 30).
    H. Eichenherr, J. Honerkamp: J.Math.Phys. 22, 374–376 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  35. 31).
    H. Eichenherr: Phys.Lett. 90 B, 121–124 (1980)Google Scholar
  36. 32).
    R. D'Auria, T. Regge, S. Sciuto: Nucl.Phys. B 171, 167–188 (1980)MathSciNetCrossRefGoogle Scholar
  37. 32a).
    M. Caselle, R. Megna, S. Sciuto: Nuov.Cim. 63A, 339–352 (1981)MathSciNetCrossRefGoogle Scholar
  38. 33).
    I.V. Cherednik: Theor.Math.Phys. 38, 120–124 (1979); 41, 997–1002 (1979)MathSciNetCrossRefGoogle Scholar
  39. 34).
    K. Scheler: Z.Phys.C-Particles and Fields 6, 365–369 (1980)MathSciNetCrossRefGoogle Scholar
  40. 35).
    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)Google Scholar
  41. 36).
    R. Flume, S. Meyer: Phys.Lett. 85 B, 353–356 (1979)Google Scholar
  42. 37).
    S. Kobayashi, K. Nomizu: "Foundations of Differential Geometry." Interscience, New York, 1963 (Vol.1) and 1969 (Vol.2).zbMATHGoogle Scholar
  43. 38).
    L.D. Faddeev, M.A. Semenov-Tjan'Shansky: Leningrad University Vestnik 13, 81–88 (1977) (in Russian)Google Scholar
  44. 39).
    E. Cartan: Bull.Soc.Math.France 54, 214–264 (1926); 55, 114–134 (1927)MathSciNetGoogle Scholar
  45. 40).
    S. Helgason: "Differential Geometry, Lie Groups, and Symmetric Spaces." Academic Press, New York, 1978.zbMATHGoogle Scholar
  46. 41).
    S.B. Myers, N. Steenrod: Ann.Math. 40, 400–416 (1939)MathSciNetCrossRefGoogle Scholar
  47. 42).
    W.H. Greub: "Linear Algebra." Springer-Verlag, Berlin-Heidelberg-New York, 1967.zbMATHCrossRefGoogle Scholar
  48. 43).
    D. Ferus: Math.Ann. 247, 81–93 (1980)MathSciNetzbMATHCrossRefGoogle Scholar
  49. 44).
    M. Lüscher: Nucl.Phys. B 135, 1–19 (1978)CrossRefGoogle Scholar
  50. 45).
    E. Abdalla, M.C.B. Abdalla, M. Gomes: Phys.Rev. D 23, 1800–1805 (1981)Google Scholar
  51. 46).
    E. Abdalla, M. Forger, M. Gomes: Nucl.Phys. B 210 [FS 6], 181–192 (1982)CrossRefGoogle Scholar
  52. 47).
    A.M. Polyakov: Phys.Lett. 72 B, 224–226 (1977)MathSciNetGoogle Scholar
  53. 48).
    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)Google Scholar
  54. 48a).
    J.H. Lowenstein, E.R. Speer: Nucl.Phys. B 158, 397–409 (1979)CrossRefGoogle Scholar
  55. 49).
    R. Heidenreich, H. Kluberg-Stern: Nucl.Phys. B 182, 205–241 (1981)CrossRefGoogle Scholar
  56. 49a).
    R. Heidenreich: "The Polyakov Currents in the Perturbative Phase of the Nonlinear O(N) Sigma Model." PhD thesis, Freie Universität Berlin, 1980 (unpublished)Google Scholar
  57. 50).
    Y.Y. Goldschmidt, E. Witten: Phys.Lett. 91 B, 392–396 (1980)MathSciNetGoogle Scholar
  58. 51).
    A.B. Zamolodchikov, Al.B. Zamolodchikov: Nucl.Phys. B 133, 525–535 (1978)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Michael Forger
    • 1
  1. 1.Fakultät für PhysikUniversität FreiburgFreiburgGermany

Personalised recommendations