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Communications in Mathematical Physics

, Volume 72, Issue 1, pp 77–102 | Cite as

Local theory of solutions for the 0(2k+1) σ-model

  • H. J. Borchers
  • W. D. Garber
Article

Abstract

We develop a theory of solutionsn for the Euclidean nonlinear 0(2k+1)σ-model for arbitraryk and for a regionG⊂ℝ2. We consider a subclass of solutions characterized by a condition which is fulfilled, forG=ℝ2, by thosen that live on the Riemann sphere S2⊃ℝ2. We are able to characterize this class completely in terms ofk meromorphic functions, and we give an explicit inductive procedure which allows us to calculate all 0(2k+1) solutions from the trivial 0(1) solutions.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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.

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References

  1. 1.
    Garber, W.D., Ruijsenaars, S.N.M., Seiler, E., Burns, D.: Ann. Phys.119, 305–325 (1979)Google Scholar
  2. 2.
    Borchers, H.J., Garber, W.D.: Analyticity of solutions for the 0(N) non-linear σ-model. Commun. Math. Phys. (in press)Google Scholar
  3. 3.
    Din, A.M., Zakrzewski, W.J.: Stability properties of classical solutions to non-linear σ-models. Preprint TH 2721-CERN 1979Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • H. J. Borchers
    • 1
  • W. D. Garber
    • 1
  1. 1.Institut für Theoretische PhysikUniversität GöttingenGöttingenGermany

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