More on Generalized Heisenberg Ferromagnet Models

TL;DR

This paper extends the classical Heisenberg ferromagnet model to a broader class based on Hermitian symmetric spaces, exploring its integrability, Hamiltonian structure, and gauge equivalence with nonlinear Schrödinger models.

Contribution

It introduces a generalized integrable ferromagnet model on Hermitian symmetric spaces, constructs its Lagrangian and Hamiltonian structures, and establishes gauge equivalence with nonlinear Schrödinger models.

Findings

Constructed Lagrangian and Hamiltonian for the generalized model.

Established gauge equivalence with nonlinear Schrödinger models.

Identified infinitely many conserved quantities.

Abstract

We generalize the integrable Heisenberg ferromagnet model according to each Hermitian symmetric spaces and address various new aspects of the generalized model. Using the first order formalism of generalized spins which are defined on the coadjoint orbits of arbitrary groups, we construct a Lagrangian of the generalized model from which we obtain the Hamiltonian structure explicitly in the case of $CP(N-1)$ orbit. The gauge equivalence between the generalized Heisenberg ferromagnet and the nonlinear Schr\"{o}dinger models is given. Using the equivalence, we find infinitely many conserved integrals of both models.