Augmented Algorithm for Generation of Constraints

It is found that Dirac's original consistency conditions do not suffice to generate all the secondary constraints and determine all the multipliers in front of the second-class constraints for the general singular Lagrangian sys tems. Cawley 's second counter example of Dirac's conjecture just has this feature. This may lead to the fact that the equivalence of Lagrangian and Hamiltonian formalism is not guaranteed and even dynamics of Hamil tonian formalism is not completely determined. In order to overcome the above difficulties, an augmen ted algorithm for generation of constraints-the algorithm of the extended consistency conditions is proposed. In this new algorithm, Cawley's second example is no longer a counter example of Dirac's conjecture.