Noether’s Theorem for Constrained Hamiltonian System Under Generalized Operators
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摘要:
研究了广义算子下奇异系统的Noether对称性与守恒量。首先，建立了广义算子下奇异系统的Lagrange方程，并导出该系统的初级约束，然后引入Lagrange乘子建立了广义算子下约束Hamilton方程以及相容性条件。其次，基于Hamilton作用量在无限小变换下的不变性，建立了广义算子下约束Hamilton系统的Noether定理，并给出了该系统的对称性及相应的守恒量。在特定条件下，广义算子下约束Hamilton系统的Noether守恒量可以退化为整数阶约束Hamilton系统的Noether守恒量。最后举例说明了结果的应用。
Abstract:Noether’s symmetry and conserved quantity of singular systems under generalized operators were studied. Firstly, the Lagrangian equation of singular systems under generalized operators was established, and the primary constraints on the system were derived. Then the Lagrangian multiplier was introduced to establish the constrained Hamilton equation and the compatibility condition under generalized operators. Secondly, based on the invariance of the Hamilton action under the infinitesimal transformation, Noether’s theorem for constrained Hamiltonian systems under generalized operators was established, and the symmetry and corresponding conserved quantity of the system were given. Under certain conditions, Noether’s conservation of constrained Hamiltonian systems under generalized operators can be reduced to Noether’s conservation of integer-order constrained Hamiltonian systems. Finally, an example illustrates the application of the results.
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