Effective action and vacuum expectations in nonlinear σ model

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The equations for effective action for nonlinear σ model are derived using DeWitt method in two forms - for generator of vertex parts Γ and for generator of weakly connected parts W. Loop-expansion solutions to these equations are found. It is shown that vacuum expectation values for various quantities including divergence of a Nöther current, trace of the energy-momentum tensor and so on, can be calculated by this method. Also it is shown that vacuum expectation to the sigma-field is determined by an explicit combination of tree Green function and classical solution. It is shown that the limit when coupling constant tends to zero is singular one.