Lagrangian formulation for noncommutative nonlinear systems

TL;DR

This paper develops a Lagrangian framework for noncommutative versions of the SU(2) Skyrme and O(3) nonlinear sigma models using Faddeev-Jackiw formalism, showing multiple noncommutative formulations are possible.

Contribution

It introduces a method to incorporate noncommutativity into nonlinear models and derives their Lagrangian formulations, expanding the theoretical tools for such systems.

Findings

Derived Lagrangian formulations for noncommutative models

Demonstrated multiple noncommutative versions can exist

Extended the Faddeev-Jackiw formalism to nonlinear systems

Abstract

In this work we use the well known formalism developed by Faddeev and Jackiw to introduce noncommutativity within two nonlinear systems, the SU(2) Skyrme and O(3) nonlinear sigma models. The final result is the Lagrangian formulations for the noncommutative versions of both models. The possibility of obtaining different noncommutative versions for these nonlinear systems is demonstrated.