On Dirac's conjecture for Hamiltonian systems with first- and second-class constraints

It is shown for a wide class of systems in the framework of the total Hamiltonian procedure that all first-class constraints generate canonical transformations connecting physically equivalent states. It occurs whenever the constraints arising in the Dirac algorithm are effective when considered in the functional form as they appear in the consistency conditions. The property of hereditary separation between first- and second-class constraints also follows from the above condition. General Poisson-brackets relations among constraints in the representation used here are also obtained. The sources of anomalies in the hereditary property reported in the literature are identified.