Besed on the symmetry properties of constrained Hamiltonian system,we present one other example to show that Dirac’s conjecture fails in a different way than other examples in that there is no linearization of constraint in this problem.A clear discussion is made on the relationships of the coefficients connecting with the first-class constraints in the gauge generator for a constrained Hamiltonian system.The results of this counterexample are also in contradiction with the other conclusions.
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