A new approach to instanton calculations in the O(3) nonlinear sigma model

TL;DR

This paper develops a novel method for calculating instantons in the O(3) nonlinear sigma model on cylindrical spacetime, addressing divergence issues by incorporating boundary conditions and boundary states.

Contribution

It constructs all instantons in the model on cylindrical spacetime, linking the scale parameter to boundary conditions, and proposes a way to resolve divergence problems in instanton gases.

Findings

Constructed all instantons on cylindrical spacetime.

Linked instanton scale parameter to boundary conditions.

Proposed a method to cure divergence in instanton gases.

Abstract

We construct all instantons in the \nlsig\ on a cylindrical space-time, known not to exist on a finite time interval. The scale parameter, $\rho$, is related to the boundary condition in time. This may cure the $\rho\rightarrow0$ divergent instanton gas, through a proper inclusion of in and out states in the path integral.