Exchange operators and extended Heisenberg algebra for the three-body Calogero-Marchioro-Wolfes problem

TL;DR

This paper extends the exchange operator formalism to the three-body Calogero-Marchioro-Wolfes problem, revealing a $D_6$-extended Heisenberg algebra structure and demonstrating its complete integrability.

Contribution

It introduces a novel extension of the exchange operator formalism to a more complex three-body system and identifies its algebraic structure.

Findings

Extension of exchange operator formalism to three-body system

Identification of $D_6$-extended Heisenberg algebra

Proof of complete integrability

Abstract

The exchange operator formalism previously introduced for the Calogero problem is extended to the three-body Calogero-Marchioro-Wolfes one. In the absence of oscillator potential, the Hamiltonian of the latter is interpreted as a free particle Hamiltonian, expressed in terms of generalized momenta. In the presence of oscillator potential, it is regarded as a free modified boson Hamiltonian. The modified boson operators are shown to belong to a $D_6$-extended Heisenberg algebra. A proof of complete integrability is also provided.