Invariants of the spherical sector in conformal mechanics
Tigran Hakobyan, Olaf Lechtenfeld, Armen Nersessian, Armen Saghatelian
TL;DR
This paper links the constants of motion in conformal mechanics to those in its spherical sector, identifying the complete set of invariants for the cuboctahedric Higgs oscillator, a key component of the Calogero model.
Contribution
It establishes a direct relation between conformal mechanics and its spherical part, providing the full set of invariants for the cuboctahedric Higgs oscillator.
Findings
Complete set of constants of motion for the cuboctahedric Higgs oscillator identified
Relation between conformal mechanics and spherical invariants established
Insights into the integrability of the Calogero model obtained
Abstract
A direct relation is established between the constants of motion for conformal mechanics and those for its spherical part. In this way we find the complete set of functionally independent constants of motion for the so-called cuboctahedric Higgs oscillator, which is just the spherical part of the rational A_3 Calogero model (describing four Calogero particles after decoupling their center of mass).
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