Quantization of planar ferromagnets in the Chern–Simons representation

We formulate the two-dimensional planar classical continuous Heisenberg spin model as a constrained Chern–Simons gauged nonlinear Schrödinger system. Several physical consequences in the framework of the anyon field theory are discussed. We study the hamiltonian structure of the model, which is quantized using the gauge invariant approach. A preliminary study of the quantum states is presented.