Third order equations of motion and the Ostrogradsky instability
Third order equations of motion and the Ostrogradsky instability
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DOI：
10.1103/physrevd.91.085009
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发表时间：
2014-11
影响因子：
5
通讯作者：
H. Motohashi;T. Suyama
中科院分区：
文献类型：
--
作者：
H. Motohashi;T. Suyama
已知任何含时间导数项高于一阶的非简并拉格朗日量都存在Ostrogradsky不稳定性，正、负能量自由度的病态激发。我们证明，在点粒子解析力学的框架内，任何三阶运动方程的拉格朗日量，只要避开了非简并条件，仍然会导致Ostrogradsky不稳定性。推广到高奇阶运动方程的情况也被考虑。
It is known that any nondegenerate Lagrangian containing time derivative terms higher than first order suffers from the Ostrogradsky instability, pathological excitation of positive and negative energy degrees of freedom. We show that, within the framework of analytical mechanics of point particles, any Lagrangian for third order equations of motion, which evades the nondegeneracy condition, still leads to the Ostrogradsky instability. Extension to the case of higher odd order equations of motion is also considered.