An Improved Harmonic Map Ansatz

TL;DR

This paper extends the rational map ansatz for the SU(2) Skyrme model by allowing the profile function to depend on additional variables, resulting in more accurate energy approximations for certain configurations.

Contribution

The authors generalize the rational map ansatz by incorporating a profile function dependent on $z$ and $ar{z}$, improving energy estimates for Skyrme model solutions.

Findings

Lowered energy estimates for B=2,3,4 configurations

Profile functions show dependence on $z$ and $ar{z}$

Potential extension to higher SU(N) models

Abstract

The rational map ansatz of Houghton et al \cite{HMS} is generalised by allowing the profile function, usually a function of $r$, to depend also on $z$ and $\bar{z}$. It is shown that, within this ansatz, the energies of the lowest $B=2,3,4$ field configurations of the SU(2) Skyrme model are closer to the corresponding values of the true solutions of the model than those obtained within the original rational map ansatz. In particular, we present plots of the profile functions which do exhibit their dependence on $ z$ and $\bar{z}$. The obvious generalisation of the ansatz to higher SU(N) models involving the introduction of more projectors is briefly mentioned.