Journal of Soviet Mathematics

, Volume 40, Issue 1, pp 149–155 | Cite as

Quasiconformal instantons

  • M. G. Tseitlin


One presents a two-dimensional conformally invariant model, in which the usual instantons (solutions of the Cauchy-Riemann equations) are replaced by quasiconformal mappings. All the usual properties of instantons are preserved. The space of the moduli of these solutions is related in a natural manner to the Teichmuller space.


Invariant Model Quasiconformal Mapping Natural Manner Usual Property Teichmuller Space 
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Literature cited

  1. 1.
    S. Hawkins, “Topological structure of the Universe,” Nucl. Phys.,B244, No. 1, 135–155 (1984).Google Scholar
  2. 2.
    P. Blanchard, “Complex analytic dynamics on the Riemann sphere,” Bull. Am. Math. Soc.,11, No. 1, 85–141 (1984).Google Scholar
  3. 3.
    M. F. Atiyah and R. Bott, “The Yang-Mills equations over Riemann surfaces,” Philos. Trans. R. Soc.,A308, 523–615 (1983).Google Scholar
  4. 4.
    O. Alvarez, “Theory of strings with boundaries: fluctuations, topology and quantum geometry,” Nuclear Phys.,B216, No. 1, 125–184 (1983).Google Scholar
  5. 5.
    J. Eells and L. Lemaire, “A report on harmonic maps,” Bull. London Math. Soc.,10, No. 1, 125–184 (1983).Google Scholar
  6. 6.
    H. Brezis and J.-M. Coron, “Large solutions for harmonic maps in two dimensions,” Commun. Math. Phys.,92, No. 2, 203–215 (1983).Google Scholar
  7. 7.
    M. G. Tseitlin, “Explicit solutions of O(3) and O(2, 1) chiral models and the associated equations of the two-dimensional Toda chain and the Ernst equation, when the solutions are parametrized by arbitrary functions,” Teor. Mat. Fiz.,57, No. 2, 238–248 (1983).Google Scholar
  8. 8.
    V. E. Chelnokov and M. G. Zeitlin, “The elliptic solution of the sinh-Gordon equation,” Phys. Lett.,99A, No. 4, 147–149 (1983); “Two explicit unconnected sets of elliptic solutions parametrized by an arbitrary function for the two-dimensional Toda chain A1 (1),” Phys. Lett.102A, No. 7, 276–278 (1984).Google Scholar
  9. 9.
    J. Eells and J. C. Wood, “Harmonic maps from surfaces to complex projective spaces,” Adv. Math.,49, No. 3, 217–263 (1983).Google Scholar
  10. 10.
    A. M. Perelomov, “Kähler chiral models,” Commun. Math. Phys.,63, No. 3, 237–243 (1978).Google Scholar
  11. 11.
    L. Bers, “Finite dimensional Teichmuller spaces and generalizations,” Bull Am. Math. Soc.,5, No. 2, 131–172 (1981).Google Scholar
  12. 12.
    M. G. Tseitlin, “The solution of two-dimensional Einstein equations, parametrized by arbitrary functions and the O(2, 1) σ-model,” in: Proc. VI Sov. Grav. Conf., Moscow (1984), Vol. 1, pp. 116–117; “The solution of two-dimensional Einstein equations with substance, parametrized by an arbitrary function,” in: Proc. VI Sov. Grav. Conf., Moscow (1984), Vol. 1, pp. 114–115.Google Scholar
  13. 13.
    V. E. Chelnokov and M. G. Zeitlin, “O(2, 1) σ-model generates the solution of the two-dimensional Einstein equation parametrized by arbitrary functions,” Phys. Lett.,104A, No. 6, 7, 329–334 (1984).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • M. G. Tseitlin

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