Hamiltonian approach to isospinning ${\mathbb C}P^2$ solitons

TL;DR

This paper develops a Hamiltonian framework to analyze isospinning ${ m C}P^2$ solitons in 2+1 dimensions, revealing their stabilization mechanisms and similarities to $U(1)$ Q-balls, and facilitating future ${ m C}P^N$ generalizations.

Contribution

It introduces a Hamiltonian approach to ${ m C}P^2$ solitons, clarifying their stabilization and extending the analysis to higher symmetry groups.

Findings

Hamiltonian formalism excludes unobservable parameters.

Revealed non-topological stabilization mechanisms.

Established similarities with $U(1)$ Q-balls.

Abstract

Isorotating ${\mathbb C}P^2$ Q-solitons in $2+1$ dimensions were studied. Hamiltonian formalism as a more physically meaningful yet fairly demanding approach was adopted during the investigation, which helped to exclude unobservable parameters such as angular frequencies and Lagrangian. This approach also highlighted the non-topological nature of the stabilization mechanism and revealed a number of similarities between well-known $U(1)$ Q-balls and ${\mathbb C}P^2$ isospinning solitons, thus rendering the latter a suitable extension of the former for the case of higher Lagrangian symmetry group and paving the way for further ${\mathbb C}P^N$ generalizations. Due to the peculiarities of the model, numerical optimisation algorithms were chosen to obtain the solutions.