Bosonization, coherent states and semiclassical quantum Hall skyrmions

Abstract

We bosonize (2+1)-dimensional fermionic theory using coherent states. The gauge-invariant subspace ofboson–Chern–Simons Hilbert space is mapped to fermionic Hilbert space. This subspace isthen equipped with a coherent state basis. These coherent states are labelled by a dynamicspinor field. The label manifold could be assigned a physical meaning in terms of densityand spin density. A path-integral representation of the evolution operator in terms of thesephysical variables is given. The corresponding classical theory when restricted to LLL isdescribed by spin fluctuations alone and is found to be the NLSM with Hopf term. Theformalism developed here is suitable to study quantum Hall skyrmions semiclassicallyand/or beyond the hydrodynamic limit. The effects of Landau level mixing orthe presence of slowly varying external fields can also be easily incorporated.