On the calculation of the vacuum energy density in sigma models

The vacuum energy density is calculated for the O(N) nonlinear sigma models in two dimensions. To obtain εvac we assume that each point of the space in which non-perturbative fields are determined can be replaced by a sphere S2 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.