The Group-Theoretical Classification of Some Multiparticle States in the Presence of Magnetic Field and Periodic Potential

Details The Group-Theoretical Classification of Some Multiparticle States in the Presence of Magnetic Field and Periodic Potential The Group-Theoretical Classification of Some Multiparticle States in the Presence of Magnetic Field and Periodic Potential

2002-12-14

arxiv.org/abs/cond-mat/0212342v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

7 pages, presented at 7th WigSym (College Park, MD, USA, Aug 2001), revtex 4

Scientific paper

The group-theoretical classification of multiparticle states(pairs of particles and charged excitons X^+-) is based on considerations of products of irreducible projective representations of the two-dimensional translation group. The states of a pair particle-antiparticle are non-degenerate, whereas, for a given Born-von Karman period N, degeneracy of pair states is N andthree-particle states are N^2-fold degenerated. The symmetrization of states with respect to particles transposition is considered. Three symmetry adapted bases for trions are considered: (i) the first is obtained from a direct conjugation of three representations; (ii) in the second approach the states of a electrically neutral pair particle-antiparticle are determined in the first step; (iii) the third possibility is to consider a pair of identical particles in the first step. In the discussion presented the Landau gauge A=[0,Hx,0] is used, but it is shown that the results obtained are gauge-independent. In addition the relation between changes of a chosen gauge and local basis transformations are discussed.

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