Abstract
The limit of the large Coulomb energy compare the cyclotron energy is considered. It is possible to relate the electron density with the analytical properties of one electron Green function and show that one electron gap exists at integer fillings of Landau level. The energy of collective excitations of plasmon type is calculated at small momenta. It is shown that the activation energy of Skyrmion-antiskyrmion pairs and the energy of spin waves is proportional to the cyclotron energy in this limit.
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