Yong-Long Wang, Chang-Tan Xu, Hua Jiang, Wei-Tao Lu, Hong-Zhe Pan
We prove the validity of the Dirac conjecture generally by adding the total time derivatives of all constraints to the Lagrangian step by step. It is worthy to state that the total time derivatives added to the original Lagrangian can turn up some constraints, and discover the symmetries hidden in the original Lagrangian. For a constrained system, the extended Hamiltonian $H_E$ contains more constraints, and shows more symmetries. We discuss the Cawley's counterexample, and prove it not a real one to the Dirac conjecture. And we offer an example, its extended Hamiltonian is better that its total Hamiltonian for its Lagrangian.
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http://arxiv.org/abs/1306.3580
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