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.
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Borchers, H.J., Garber, W.D.: Analyticity of solutions for the 0(N) non-linear σ-model. Commun. Math. Phys. (in press)
Din, A.M., Zakrzewski, W.J.: Stability properties of classical solutions to non-linear σ-models. Preprint TH 2721-CERN 1979
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Communicated by R. Stora
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Borchers, H.J., Garber, W.D. Local theory of solutions for the 0(2k+1) σ-model. Commun.Math. Phys. 72, 77–102 (1980). https://doi.org/10.1007/BF01200112
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DOI: https://doi.org/10.1007/BF01200112