QUANTUM INTEGRABILITY AND ACTION OPERATORS IN SPIN DYNAMICS

A new formulation of the quantum integrability condition for spin syst ems is proposed. It eliminates the ambiguities inherent in formulation s derived from a direct transcription of the classical integrability c riterion. In the new formulation, quantum integrability of an N-spin s ystem depends on the existence of a unitary transformation which expre sses the Hamiltonian as-a function of N action operators. All operator s are understood to be algebraic expressions of the spin components wi th no restriction to any finite-dimensional matrix representation. The consequences of quantum (non)integrability on the structure of quantu m invariants are discussed in comparison with the consequences of clas sical (non)integrability on the corresponding classical invariants. Ou r results indicate that quantum integrability is universal for systems with N=1 and contingent for systems with N greater than or equal to 2 .