Bosonization of a 2D Landau level

We study a two-dimensional electron gas in a quantizing magnetic field.
We focus on the case when only the lowest Landau level is occupied.
It is shown that lowest Landau level fermion field operator can be presented as a coherent state, consistent with the one-dimensional bosonization. This is due to the fact that the Fock space of the lowest Landau level is one-dimensional.
Coherenet state representaion allows to bosonize filled Landau level and derive a low-energy theory of edge excitations, consistent with chiral Fermi and chiral Luttinger liquids descriptions.
It is shown, the Coulomb interaction results in local in space dispersion for electrons in the bulk of the Landau level.