This article is cited in 4 papers

Systems of $sl(2,\mathbb{C})$ tops as two-particle systems

A. V. Smirnov

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: We show that Euler–Arnold tops on the algebra $sl(2,\mathbb C)$ are equivalent to a two-particle system of Calogero type. We show that an arbitrary quadratic Hamiltonian of an $sl(2,\mathbb C)$ top can be reduced to one of the three canonical Hamiltonians using the automorphism group of the algebra. For each canonical Hamiltonian, we obtain the corresponding two-particle system and write the bosonization formulas for the coadjoint orbits explicitly. We discuss the relation of the obtained formulas to nondynamical Antonov–Zabrodin–Hasegawa $R$-matrices for Calogero–Sutherland systems.

Keywords: integrable system, Euler–Arnold top, Calogero–Moser system.

Received: 18.10.2007

DOI: 10.4213/tmf6261

 English version: Theoretical and Mathematical Physics, 2008, 157:1, 1370–1382

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