This paper analyzes the constraint structure of a class of degenerate second-order particle Lagrangian that includes chiral oscillator, noncommutative oscillator, and two examples from reduced topologically massive gravity. For even-dimensional configuration spaces with maximal nondegeneracy, Dirac bracket is defined solely by coefficient field of highest derivative whereas for odd dimensions almost all fields may contribute. Ostrogradskii’s theorem on energy instability is discussed. Results of Dirac analysis are used to identify ghost degrees of freedom. Translational symmetries are used to construct first-order variational formalisms for oscillator examples, thereby making them ghost-free.

中文翻译：

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一类二阶退化拉格朗日量的狄拉克分析和奥斯特罗格拉茨基定理

本文分析了一类退化二阶粒子拉格朗日的约束结构，包括手征振子、非对易振子和两个简化拓扑大质量引力的例子。对于具有最大非退化性的偶数维配置空间，狄拉克括号仅由最高导数的系数场定义，而对于奇数维，几乎所有场都可能有贡献。讨论了 Ostrogradskii 关于能量不稳定性的定理。狄拉克分析的结果用于识别重影自由度。平移对称性用于构造振荡器示例的一阶变分形式，从而使它们无重影。