Collective fields, Calogero-Sutherland model and generalized matrix models

Details Collective fields, Calogero-Sutherland model and generalized matrix models Collective fields, Calogero-Sutherland model and generalized matrix models

1994-11-08

arxiv.org/abs/hep-th/9411053v3

Phys. Lett. B347 (1995) 49

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, latex, no figures, a few references added

Scientific paper

10.1016/0370-2693(95)00055-P

On the basis of the collective field method, we analyze the Calogero--Sutherland model (CSM) and the Selberg--Aomoto integral, which defines, in particular case, the partition function of the matrix models. Vertex operator realizations for some of the eigenstates (the Jack polynomials) of the CSM Hamiltonian are obtained. We derive Virasoro constraint for the generalized matrix models and indicate relations with the CSM operators. Similar results are presented for the $q$--deformed case (the Macdonald operator and polynomials), which gives the generating functional of infinitely many conserved charges in the CSM.

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