`Composite particles' and the eigenstates of Calogero-Sutherland and Ruijsenaars-Schneider

Details `Composite particles' and the eigenstates of Calogero-Sutherland and Ruijsenaars-Schneider `Composite particles' and the eigenstates of Calogero-Sutherland and Ruijsenaars-Schneider

1999-07-27

arxiv.org/abs/cond-mat/9907411v2

Physics

Condensed Matter

latex calcomp2.tex, 5 files, 30 pages [SPhT-T99/080], submitted to J. Math. Phys

Scientific paper

10.1063/1.1286050

We establish a one-to-one correspondance between the ''composite particles'' with $N$ particles and the Young tableaux with at most $N$ rows. We apply this correspondance to the models of Calogero-Sutherland and Ruijsenaars-Schneider and we obtain a momentum space representation of the ''composite particles'' in terms of creation operators attached to the Young tableaux. Using the technique of bosonisation, we obtain a position space representation of the ''composite particles'' in terms of products of vertex operators. In the special case where the ''composite particles'' are bosons and if we add one extra quasiparticle or quasihole, we construct the ground state wave functions corresponding to the Jain series $\nu =p/(2np\pm 1) $ of the fractional quantum Hall effect.

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