On the calculation of the vacuum energy density in sigma models

Abstract The vacuum energy density is calculated for the O ( N ) nonlinear sigma models in two dimensions. To obtain e vac we assume that each point of the space in which non-perturbative fields are determined can be replaced by a sphere S 2 having a small radius r which approaches zero at the very end of the calculation. This assumption allows to get the classical fields generating v.e.v. of the trace of the energy-momentum tensor.