Quantum Current Algebra Symmetries and Integrable Many-Particle Schrödinger Type Quantum Hamiltonian Operators

Abstract

Based on the G. Goldin’s quantum current algebra symmetry representation theory, have succeeded in explaining a hidden relationship between the quantum many-particle Hamiltonian operators, defined in the Fock space, their factorized structure and integrability. Interesting for applications quantum oscillatory Hamiltonian operators are considered, the quantum symmetries of the integrable quantum Calogero-Sutherland model are analyzed in detail.