On the Calculation of the Vacuum Energy Density in Sigma Models

TL;DR

This paper calculates the vacuum energy density in two-dimensional $O(N)$ nonlinear sigma models using a novel approach that replaces points in space with small spheres to derive classical fields.

Contribution

It introduces a new method of approximating non-perturbative fields by replacing points with small spheres to compute vacuum energy density.

Findings

Derived an expression for vacuum energy density in sigma models.

Provided a new technique for handling non-perturbative effects.

Connected classical field configurations to quantum vacuum properties.

Abstract

The vacuum energy density is calculated for the $O(N)$ nonlinear sigma models in two dimensions. To obtain $\varepsilon_{vac}$ we assume that each point of the space in which non-perturbative f\/ields 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 f\/ields generating v.e.v. of the trace of the energy-momentum tensor.