Physics and Mathematics of Calogero particles

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Alexios P. Polychronakos This is my paper · ORCID

classification hep-thcond-mat.othermath-phmath.MP

keywords calogerocalogero-likecelebratedchainsfamilygivemathematicalmathematics

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We give a review of the mathematical and physical properties of the celebrated family of Calogero-like models and related spin chains.

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${\cal N}{=}\,4$ supersymmetric multiparticle systems based on indecomposable multiplets
hep-th 2026-07 unverdicted novelty 7.0 of 10

Nonlinear indecomposable multiplets (1,4,3)⊃+(4,4,0) produce new N=4 supersymmetric deformations of U(2)-spin rational Calogero models invariant under OSp(4|2), plus a near-equivalent hyperbolic version.
A superintegrable quantum field theory
nlin.SI 2025-11 unverdicted novelty 6.0 of 10

The quantum cubic Szegő equation exhibits integer spectra for its Hamiltonian and conserved hierarchies, indicating superintegrability beyond ordinary quantum integrability.