The O(N) Nonlinear Sigma Model in the Functional Schr\"{o}dinger Picture

TL;DR

This paper develops a functional Schr"{o}dinger picture formalism for the (1+1)-dimensional O(N) nonlinear sigma model, calculating the energy density to two-loop order and deriving the nonperturbative mass gap using a Gaussian wave functional.

Contribution

It introduces a novel functional Schr"{o}dinger picture approach combined with variational methods to analyze the ground state of the nonlinear sigma model.

Findings

Calculated energy density to two-loop order.

Derived the nonperturbative mass gap.

Provided a transparent description of the ground state characteristics.

Abstract

We present a functional Schr\"{o}dinger picture formalism of the (1+1)-dimensional $O(N) $ nonlinear sigma model. The energy density has been calculated to two-loop order using the wave functional of a gaussian form, and from which the nonperturbative mass gap of the boson fields has been obtained. The functional Schr\"{o}dinger picture approach combined with the variational technique is shownto describe the characteristics of the ground state of the nonlinear sigma model in a transparent way.