Integrability, intertwiners and non-linear algebras in Calogero models

Abstract

For the rational quantum Calogero systems of type $A_1\oplus A_2$, $A{D}_3$ and $B{C}_3$, we explicitly present complete sets of independent conserved charges and their nonlinear algebras. Using intertwining (or shift) operators, we include the extra `odd' charges appearing for integral couplings. Formulae for the energy eigenstates are used to tabulate the low-level wave functions.

arXiv comment16 pages

References in corpus (6)

• Physics and Mathematics of Calogero particles
• Hidden symmetry of the quantum Calogero-Moser system
• Nonlinear supersymmetry in the quantum Calogero model
• $\mathcal{P}\mathcal{T}$ deformation of angular Calogero models
• $\mathcal{P}\mathcal{T}$ deformation of Calogero-Sutherland models
• Exchange interactions, Yang-Baxter relations and transparent particles

Cited by in corpus (1)

• Algebraic integrability of $\mathcal{P}\mathcal{T}$-deformed Calogero models