The group-theoretical classification of states of identical particle pairs is presented. Then obt... more 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^2-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.
The group-theoretical classification of multiparticle states(pairs of particles and charged excit... more 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 additi...
The group-theoretical classification of states of identical particle pairs is presented. Then obt... more 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^2-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.
The group-theoretical classification of multiparticle states(pairs of particles and charged excit... more 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 additi...
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Papers by Wojciech Florek