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


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.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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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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