  Quantum canonical transformations are defined in analogy to classical
canonical transformations as changes of the phase space variables which
preserve the Dirac bracket structure. In themselves, they are neither unitary
nor non-unitary. A definition of quantum integrability in terms of canonical
transformations is proposed which includes systems which have fewer commuting
integrals of motion than degrees of freedom. The important role of non-unitary
transformations in integrability is discussed.
