Hamiltonian Formulation of Quantum Hall Skyrmions with Hopf Term

TL;DR

This paper develops a Hamiltonian framework for quantum Hall skyrmions incorporating the Hopf term, revealing new algebraic structures and physical insights relevant to skyrmion behavior in quantum Hall systems.

Contribution

It introduces a Hamiltonian analysis of the nonlinear sigma model with Hopf term in $CP^1$ variables, highlighting how the Hopf term modifies the spin algebra and system dynamics.

Findings

Hopf term significantly alters the Hamiltonian structure.

New momentum and angular momentum generators are identified.

The spin algebra is modified, providing new physical interpretations.

Abstract

We study the nonrelativistic nonlinear sigma model with Hopf term in this paper. This is an important issue beacuse of its relation to the currently interesting studies in skyrmions in quantum Hall systems. We perform the Hamiltonian analysis of this system in $CP^1$ variables. When the coefficient of the Hopf term becomes zero we get the Landau-Lifshitz description of the ferromagnets. The addition of Hopf term dramatically alters the Hamiltonian analysis. The spin algebra is modified giving a new structure and interpretation to the system. We point out momentum and angular momentum generators and new features they bring in to the system.