Two-dimensional electron gas in a periodic potential and external magnetic field: states of pairs and three-particle systems

The group-theoretical classification of states of identical particle pairs is presented. Then obtained states are coupled with those of an antiparticle to construct states of a three-particle system. Investigations are performed using products of irreducible projective representations of the 2D translation group. For a given BvK period N degeneracy of pair states is N , whereas three-particle states are N-fold degenerated. It has to be underlined that the case of even N is more complicated since pair states are labelled by four inequivalent irreducible projective representations. The problem of symmetry properties with respect to particles transposition is briefly discussed PACS numbers: 73.20.Dx, 71.70.Di, 02.20.-a