Hamiltonian Formulation of Quantum Hall Skyrmions with Hopf Term

Abstract

We study the nonrelativistic nonlinear sigma model with Hopf term in this letter. This is an important issue because of its relation to the currently interesting studies in skyrmions in quantum Hall systems. We perform the Hamiltonian analysis of this system in CP1 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 into the system.