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“Composite particles” and the eigenstates of Calogero-Sutherland and Ruijsenaars-Schneider. (English) Zbl 0971.81197

Summary: We establish a one-to-one correspondence between the “composite particles” with \(N\) particles and the Young tableaux with at most \(N\) rows. We apply this correspondence 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 bosonization, 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.

MSC:

81V70 Many-body theory; quantum Hall effect
81R12 Groups and algebras in quantum theory and relations with integrable systems
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
05E10 Combinatorial aspects of representation theory
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