Two body systems from sl(2,C)-tops

TL;DR

This paper demonstrates that sl(2,C) Euler-Arnold tops are equivalent to Calogero-Moser type two-body systems, classifies their Hamiltonians, and provides explicit bosonisation formulas and R-matrix relations.

Contribution

It establishes the equivalence between sl(2,C) tops and two-body Calogero-Moser systems, classifies canonical Hamiltonians, and derives explicit formulas and relations.

Findings

Classification of three canonical Hamiltonians for sl(2,C) tops

Explicit bosonisation formulas for each case

Connections with Antonov-Zabrodin-Hasegawa R-matrix

Abstract

It is shown that sl(2,$\mathbb{C}$) Euler-Arnold tops are equivalent to the two-body systems of Calogero-Moser type. We prove that generic Hamiltonians of sl(2,$\mathbb{C}$) tops are equivalent to one of three canonical Hamiltonians. For all canonical Hamiltonians the corresponding two-body system is found. Bosonisation formulas for each case are obtained explicitly. Relations with Antonov-Zabrodin-Hasegawa R-matrix are discussed.