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INTERACTING FAMILIES OF CALOGERO-TYPE PARTICLES AND SU(1,1) ALGEBRA

S. MELJANAC

Rudjer Bošković Institute, Bijenička c.54, HR-10002 Zagreb, Croatia

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M. MILEKOVIĆ

Theoretical Physics Department, Faculty of Science, P.O.B. 331, Bijenička c.32, HR-10002 Zagreb, Croatia

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A. SAMSAROV

Rudjer Bošković Institute, Bijenička c.54, HR-10002 Zagreb, Croatia

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M. STOJIĆ

Rudjer Bošković Institute, Bijenička c.54, HR-10002 Zagreb, Croatia

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https://doi.org/10.1142/S0217984904007165Cited by:10 (Source: Crossref)

Abstract

We study a one-dimensional model with F interacting families of Calogero-type particles. The model includes harmonic, two-body and three-body interactions. We emphasize the universal SU(1,1) structure of the model. We show how SU(1,1) generators for the whole system are composed of SU(1,1) generators of arbitrary subsystems. We find the exact eigenenergies corresponding to a class of the exact eigenstates of the F-family model. By imposing the conditions for the absence of the three-body interaction, we find certain relations between the coupling constants. Finally, we establish some relations of equivalence between two systems containing F families of Calogero-type particles.

Keywords:

PACS: 03.65.Fd, 03.65.Sq, 05.30.Pr

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