Integrability, intertwiners and non-linear algebras in Calogero models

Abstract

Abstract For the rational quantum Calogero systems of type A 1⊕A 2, AD 3 and BC 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. Formulæ for the energy eigenstates are used to tabulate the low-level wave functions.

Keywords

• Integrable Field Theories
• Conformal and W Symmetry
• Discrete Symmetries
• Integrable Hierarchies