Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2002-12-17
Acta Phys. Polon. A 99 (2001) 601
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
8 pages, LaTeX 2e
Scientific paper
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.
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