Local theory of solutions for the 0(2k+1) σ-model
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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.
KeywordsNeural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing
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