【摘要】 由扩展正则作用量导出了高阶微商奇异Lagrange量系统的扩展正则Noether恒等式 .从广义约束Hamilton系统相空间中对称性分析 ,给出高阶微商系统Dirac猜想的一个反例 .用正则Noether定理、正则Noether恒等式和扩展正则Noether恒等式说明在此反例中Dirac猜想失效 ,讨论中没有将约束线性化更多还原

【Abstract】 The extended canonical Noether identities derived from an extended action in the phase space for a system with a higher-order singular Lagrangian are formulated.Based on the canonical symmetries of generalized constrained Hamiltonian systems, a counterexample to a conjecture of Dirac is given. Using the canonical first Noether theorem and canonical Noether identities and the extended canonical Noether identities, we have shown that Dirac’s conjecture fails for a system with a higher-order singular Lagrangian in which there is no linearization of constraint in our treatment.更多还原